Lie群論・表現論セミナー
過去の記録 ~02/12|次回の予定|今後の予定 02/13~
開催情報 | 火曜日 16:30~18:00 数理科学研究科棟(駒場) 126号室 |
---|---|
担当者 | 小林俊行 |
セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
過去の記録
2010年05月25日(火)
17:00-18:00 数理科学研究科棟(駒場) 126号室
5月24日(月)-28日(金)に平賀氏の集中講義が行われます
平賀郁 氏 (京都大学)
On endoscopy, packets, and invariants (JAPANESE)
5月24日(月)-28日(金)に平賀氏の集中講義が行われます
平賀郁 氏 (京都大学)
On endoscopy, packets, and invariants (JAPANESE)
[ 講演概要 ]
The theory of endoscopy came out of the Langlands functoriality and the trace formula.
In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.
I would like to talk about the connection between these topics and the endoscopy.
The theory of endoscopy came out of the Langlands functoriality and the trace formula.
In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.
I would like to talk about the connection between these topics and the endoscopy.
2010年05月18日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
B. Speh 氏 (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
B. Speh 氏 (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
[ 講演概要 ]
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \\Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \\Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
2010年05月11日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
松本久義 氏 (東京大学)
On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
松本久義 氏 (東京大学)
On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
[ 講演概要 ]
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
2010年04月27日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
大島芳樹 氏 (東京大学)
Vogan-Zuckerman加群の対称部分群に関する制限 (JAPANESE)
大島芳樹 氏 (東京大学)
Vogan-Zuckerman加群の対称部分群に関する制限 (JAPANESE)
[ 講演概要 ]
We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.
We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.
2010年04月20日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
奥田 隆幸 氏 (東京大学)
半単純対称空間におけるSL(2,R)の固有な作用 (JAPANESE)
奥田 隆幸 氏 (東京大学)
半単純対称空間におけるSL(2,R)の固有な作用 (JAPANESE)
[ 講演概要 ]
SL(2,R)が固有に作用しうる複素既約対称空間は、手塚勝貴氏によって分類されてい
る。この講演ではその一般化として、複素でない場合も含めた半単純対称空間で、SL(2,R)が固有に作用しうるものの分類を紹介する。
SL(2,R)が固有に作用しうる複素既約対称空間は、手塚勝貴氏によって分類されてい
る。この講演ではその一般化として、複素でない場合も含めた半単純対称空間で、SL(2,R)が固有に作用しうるものの分類を紹介する。
2010年04月15日(木)
16:30-18:00 数理科学研究科棟(駒場) 056号室
いつもと場所・時刻が違います
Uuganbayar Zunderiya 氏 (Nagoya University)
超幾何微分方程式系の一般化 (ENGLISH)
いつもと場所・時刻が違います
Uuganbayar Zunderiya 氏 (Nagoya University)
超幾何微分方程式系の一般化 (ENGLISH)
[ 講演概要 ]
新しい形の"超幾何微分方程式系”が関口(英)によって導入された。
この偏微分方程式系はガウス-青本-ゲルファント系を高階に一般化したものであり、
それは1937年にMayrが導入したgenericな代数方程式の解に対する微分関係式
にも端を発する。
ガウス-青本-ゲルファント系は偏微分作用素を成分とする
2x2の行列の行列式として得られる2階の微分作用素を主要項とする。
関口(英)はm x m次の行列の行列式として得られるm階の
微分作用素を用いてこの方程式系を一般化した。
この講演ではガウス-青本-ゲルファントの超幾何微分方程式系の
関口による高階化がいつホロノミー系になるかを述べ、また、その
大域解および局所解の次元についての組合せ論的な公式について解説する。
新しい形の"超幾何微分方程式系”が関口(英)によって導入された。
この偏微分方程式系はガウス-青本-ゲルファント系を高階に一般化したものであり、
それは1937年にMayrが導入したgenericな代数方程式の解に対する微分関係式
にも端を発する。
ガウス-青本-ゲルファント系は偏微分作用素を成分とする
2x2の行列の行列式として得られる2階の微分作用素を主要項とする。
関口(英)はm x m次の行列の行列式として得られるm階の
微分作用素を用いてこの方程式系を一般化した。
この講演ではガウス-青本-ゲルファントの超幾何微分方程式系の
関口による高階化がいつホロノミー系になるかを述べ、また、その
大域解および局所解の次元についての組合せ論的な公式について解説する。
2010年04月06日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
加藤周 氏 (京都大学)
On the characters of tempered modules of affine Hecke
algebras of classical type
加藤周 氏 (京都大学)
On the characters of tempered modules of affine Hecke
algebras of classical type
[ 講演概要 ]
We present an inductive algorithm to compute the characters
of tempered modules of an affine Hecke algebras of classical
types, based on a new class of representations which we call
"tempered delimits". They have some geometric origin in the
eDL correspondence.
Our new algorithm has some advantage to the Lusztig-Shoji
algorithm (which also describes the characters of tempered
modules via generalized Green functions) in the sense it
enables us to tell how the characters of tempered modules
changes as the parameters vary.
This is a joint work with Dan Ciubotaru at Utah.
We present an inductive algorithm to compute the characters
of tempered modules of an affine Hecke algebras of classical
types, based on a new class of representations which we call
"tempered delimits". They have some geometric origin in the
eDL correspondence.
Our new algorithm has some advantage to the Lusztig-Shoji
algorithm (which also describes the characters of tempered
modules via generalized Green functions) in the sense it
enables us to tell how the characters of tempered modules
changes as the parameters vary.
This is a joint work with Dan Ciubotaru at Utah.
2010年02月19日(金)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
[ 講演概要 ]
I will focus on recent advances on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups, ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1, and such that no finite union of vector subspaces is invariant by A and B. We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
I will focus on recent advances on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups, ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1, and such that no finite union of vector subspaces is invariant by A and B. We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
2010年02月02日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーとの合同で行います。いつもと場所が違います。
Fanny Kassel 氏 (Orsay)
Deformation of compact quotients of homogeneous spaces
トポロジー火曜セミナーとの合同で行います。いつもと場所が違います。
Fanny Kassel 氏 (Orsay)
Deformation of compact quotients of homogeneous spaces
[ 講演概要 ]
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.
2010年01月12日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
西岡斉治 氏 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
西岡斉治 氏 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
[ 講演概要 ]
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
[ 参考URL ]差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
2009年12月22日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
西山享 氏 (青山学院大学)
既約表現の隨伴多様体は余次元1で連結か?--- 証明の破綻とその背景
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
西山享 氏 (青山学院大学)
既約表現の隨伴多様体は余次元1で連結か?--- 証明の破綻とその背景
[ 講演概要 ]
既約 Harish-Chandra $ (g, K) $ 加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道 $ O^G $ の閉包になることはよく知られている(Joseph, Borho)。
一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は $ O^G $ の $ K $-等質ラグランジュ部分多様体の閉包になる。
それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介(もちろん間違っていない)と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。)
[ 参考URL ]既約 Harish-Chandra $ (g, K) $ 加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道 $ O^G $ の閉包になることはよく知られている(Joseph, Borho)。
一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は $ O^G $ の $ K $-等質ラグランジュ部分多様体の閉包になる。
それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介(もちろん間違っていない)と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009年12月15日(火)
17:00-18:00 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同です。この週に砂田利一氏の集中講義が行われます
砂田利一氏 氏 (明治大学理工学部)
Open Problems in Discrete Geometric Analysis
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
トポロジー火曜セミナーと合同です。この週に砂田利一氏の集中講義が行われます
砂田利一氏 氏 (明治大学理工学部)
Open Problems in Discrete Geometric Analysis
[ 講演概要 ]
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
[ 参考URL ]Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
2009年11月04日(水)
16:30-18:00 数理科学研究科棟(駒場) 128号室
同じ週の木・金に柏キャンパスで開催されるIMPU workshopの講演内容に関係しています。 http://faculty.ms.u-tokyo.ac.jp/~topology/IPMU/workshop.html
Gert Heckman 氏 (IMAPP, Faculty of Science, Radboud University Nijmegen)
Birational Hyperbolic Geometry
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
同じ週の木・金に柏キャンパスで開催されるIMPU workshopの講演内容に関係しています。 http://faculty.ms.u-tokyo.ac.jp/~topology/IPMU/workshop.html
Gert Heckman 氏 (IMAPP, Faculty of Science, Radboud University Nijmegen)
Birational Hyperbolic Geometry
[ 講演概要 ]
We study compactifications for complex ball quotients.
We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.
Then we discuss compactifications of ball quotients minus a totally geodesic divisor.
These compactifications turn up for a suitable class of period maps.
[ 参考URL ]We study compactifications for complex ball quotients.
We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.
Then we discuss compactifications of ball quotients minus a totally geodesic divisor.
These compactifications turn up for a suitable class of period maps.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009年10月15日(木)
16:30-18:00 数理科学研究科棟(駒場) 122号室
土岡俊介 氏 (RIMS, Kyoto University)
Hecke-Clifford superalgebras and crystals of type $D^{(2)}_{l}$
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
土岡俊介 氏 (RIMS, Kyoto University)
Hecke-Clifford superalgebras and crystals of type $D^{(2)}_{l}$
[ 講演概要 ]
It is known that we can sometimes describe the representation theory of ``Hecke algebra'' by ``Lie theory''. Famous examples that involve the Lie theory of type $A^{(1)}_n$ are Lascoux-Leclerc-Thibon's interpretation of Kleshchev's modular branching rule for the symmetric groups and Ariki's theorem generalizing Lascoux-Leclerc-Thibon's conjecture for the Iwahori-Hecke algebras of type A.
Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke-Clifford superalgebras and its finite-dimensional ``cyclotomic'' quotients are controlled by the Lie theory of type $A^{(2)}_{2l}$ when the quantum parameter $q$ is a primitive $(2l+1)$-th root of unity.
In this talk, we show that similar theorems hold when $q$ is a primitive $4l$-th root of unity by replacing the Lie theory of type $A^{(2)}_{2l}$ with that of type $D^{(2)}_{l}$.
[ 参考URL ]It is known that we can sometimes describe the representation theory of ``Hecke algebra'' by ``Lie theory''. Famous examples that involve the Lie theory of type $A^{(1)}_n$ are Lascoux-Leclerc-Thibon's interpretation of Kleshchev's modular branching rule for the symmetric groups and Ariki's theorem generalizing Lascoux-Leclerc-Thibon's conjecture for the Iwahori-Hecke algebras of type A.
Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke-Clifford superalgebras and its finite-dimensional ``cyclotomic'' quotients are controlled by the Lie theory of type $A^{(2)}_{2l}$ when the quantum parameter $q$ is a primitive $(2l+1)$-th root of unity.
In this talk, we show that similar theorems hold when $q$ is a primitive $4l$-th root of unity by replacing the Lie theory of type $A^{(2)}_{2l}$ with that of type $D^{(2)}_{l}$.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009年10月13日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
小寺諒介 氏 (東京大学)
Extensions between finite-dimensional simple modules over a generalized current Lie algebra
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
小寺諒介 氏 (東京大学)
Extensions between finite-dimensional simple modules over a generalized current Lie algebra
[ 講演概要 ]
$\\mathfrak{g}$を$\\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\\mathbb {C}$代数とする.
テンソル積$A \\otimes \\mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ.
一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する.
[ 参考URL ]$\\mathfrak{g}$を$\\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\\mathbb {C}$代数とする.
テンソル積$A \\otimes \\mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ.
一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009年08月12日(水)
10:00-16:30 数理科学研究科棟(駒場) 002号室
Sigurdur Helgason 氏 (MIT) 10:00-11:00
Radon Transform and some Applications
Fulton G. Gonzalez 氏 (Tufts University) 11:20-12:20
Multitemporal Wave Equations: Mean Value Solutins
Angela Pasquale 氏 (Universite Metz) 14:00-15:00
Analytic continuation of the resolvent of the Laplacian in the Euclidean settings
Decay of smooth vectors for regular representations
Sigurdur Helgason 氏 (MIT) 10:00-11:00
Radon Transform and some Applications
Fulton G. Gonzalez 氏 (Tufts University) 11:20-12:20
Multitemporal Wave Equations: Mean Value Solutins
Angela Pasquale 氏 (Universite Metz) 14:00-15:00
Analytic continuation of the resolvent of the Laplacian in the Euclidean settings
[ 講演概要 ]
We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.
Henrik Schlichtkrull 氏 (University of Copenhagen) 15:30-16:30We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.
Decay of smooth vectors for regular representations
[ 講演概要 ]
Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)
Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)
2009年06月15日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Vladimir P. Kostov 氏 (Nice大学)
On the Schur-Szeg\\"o composition of polynomials
Vladimir P. Kostov 氏 (Nice大学)
On the Schur-Szeg\\"o composition of polynomials
[ 講演概要 ]
The Schur-Szeg\\"o composition of the degree $n$ polynomials $P:=\\sum_{j=0}^na_jx^j$ and $Q:=\\sum_{j=0}^nb_jx^j$ is defined by the formula $P*Q:=\\sum_{j=0}^na_jb_jx^j/C_n^j$ where $C_n^j=n!/j!(n-j)!$. Every degree $n$ polynomial having one of its roots at $-1$ (i.e. $P=(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$) is representable as a Schur-Szeg\\"o composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$ where the numbers $a_i$ are uniquely defined up to permutation. Denote the elementary symmetric polynomials of the numbers $a_i$ by $\\sigma_1$, $\\ldots$, $\\sigma_{n-1}$. The talk will focus on some properties of the affine mapping
$$(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma_1,\\ldots ,\\sigma_{n-1})$$
The Schur-Szeg\\"o composition of the degree $n$ polynomials $P:=\\sum_{j=0}^na_jx^j$ and $Q:=\\sum_{j=0}^nb_jx^j$ is defined by the formula $P*Q:=\\sum_{j=0}^na_jb_jx^j/C_n^j$ where $C_n^j=n!/j!(n-j)!$. Every degree $n$ polynomial having one of its roots at $-1$ (i.e. $P=(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$) is representable as a Schur-Szeg\\"o composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$ where the numbers $a_i$ are uniquely defined up to permutation. Denote the elementary symmetric polynomials of the numbers $a_i$ by $\\sigma_1$, $\\ldots$, $\\sigma_{n-1}$. The talk will focus on some properties of the affine mapping
$$(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma_1,\\ldots ,\\sigma_{n-1})$$
2009年02月03日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Gombodorj Bayarmagnai 氏 (東京大学数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Gombodorj Bayarmagnai 氏 (東京大学数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)
[ 講演概要 ]
In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
[ 参考URL ]In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009年01月15日(木)
13:30-17:20 数理科学研究科棟(駒場) 050号室
大島利雄教授還暦記念研究集会
柏原正樹 氏 (京都大学数理解析研究所) 13:30-14:30
Quantization of complex manifolds
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/oshima60th200901.html
小林俊行 氏 (東京大学大学院数理科学研究科) 15:00-16:00
Global geometry on locally symmetric spaces — beyond the Riemannian case
Classification of Fuchsian systems and their connection problem
大島利雄教授還暦記念研究集会
柏原正樹 氏 (京都大学数理解析研究所) 13:30-14:30
Quantization of complex manifolds
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/oshima60th200901.html
小林俊行 氏 (東京大学大学院数理科学研究科) 15:00-16:00
Global geometry on locally symmetric spaces — beyond the Riemannian case
[ 講演概要 ]
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.
In this talk, I plan to give an exposition on the recent developments on the question about the global natures of locally non-Riemannian homogeneous spaces, with emphasis on the existence problem of compact forms, rigidity and deformation.
大島利雄 氏 (東京大学大学院数理科学研究科) 16:20-17:20The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.
In this talk, I plan to give an exposition on the recent developments on the question about the global natures of locally non-Riemannian homogeneous spaces, with emphasis on the existence problem of compact forms, rigidity and deformation.
Classification of Fuchsian systems and their connection problem
[ 講演概要 ]
We explain a classification of Fuchsian systems on the Riemann sphere together with Katz's middle convolution, Yokoyama's extension and their relation to a Kac-Moody root system discovered by Crawley-Boevey.
Then we present a beautifully unified connection formula for the solution of the Fuchsian ordinary differential equation without moduli and apply the formula to the harmonic analysis on a symmetric space.
We explain a classification of Fuchsian systems on the Riemann sphere together with Katz's middle convolution, Yokoyama's extension and their relation to a Kac-Moody root system discovered by Crawley-Boevey.
Then we present a beautifully unified connection formula for the solution of the Fuchsian ordinary differential equation without moduli and apply the formula to the harmonic analysis on a symmetric space.
2009年01月12日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
西岡斉治 氏 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
西岡斉治 氏 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
[ 講演概要 ]
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
2008年12月04日(木)
17:00-18:00 数理科学研究科棟(駒場) 056号室
いつもと開始時刻および場所が違いますのでご注意ください
Genkai Zhang 氏 (Chalmers and Gothenburg University)
Realization of quanternionic discrete series as spaces of H-holomorphic
functions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
いつもと開始時刻および場所が違いますのでご注意ください
Genkai Zhang 氏 (Chalmers and Gothenburg University)
Realization of quanternionic discrete series as spaces of H-holomorphic
functions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2008年12月02日(火)
17:00-18:00 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同で開催します. またいつもと開催時刻および開催場所が違います。
金井雅彦 氏 (名古屋大学)
消滅と剛性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
トポロジー火曜セミナーと合同で開催します. またいつもと開催時刻および開催場所が違います。
金井雅彦 氏 (名古屋大学)
消滅と剛性
[ 講演概要 ]
The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.
The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
[ 参考URL ]The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.
The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2008年11月25日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
吉野太郎 氏 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
吉野太郎 氏 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ 講演概要 ]
Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
[ 参考URL ]Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2008年11月18日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Jorge Vargas 氏 (FAMAF-CIEM, C\'ordoba)
Liouville measures and multiplicity formulae for admissible restriction of Discrete Series
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Jorge Vargas 氏 (FAMAF-CIEM, C\'ordoba)
Liouville measures and multiplicity formulae for admissible restriction of Discrete Series
[ 講演概要 ]
Let $H \\subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\\pi$ of $G.$
Let $\\Omega $ denote the coadjoint orbit of the Harish-Chandra parameter of $\\pi.$
Assume $\\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\\pi$ restricted to $H$ and push forward to $\\mathfrak h^\\star$ of the Liouville measure for $\\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
[ 参考URL ]Let $H \\subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\\pi$ of $G.$
Let $\\Omega $ denote the coadjoint orbit of the Harish-Chandra parameter of $\\pi.$
Assume $\\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\\pi$ restricted to $H$ and push forward to $\\mathfrak h^\\star$ of the Liouville measure for $\\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2008年10月28日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Joachim Hilgert 氏 (Paderborn University)
Chevalley's restriction theorem for supersymmetric Riemannian symmetric spaces
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Joachim Hilgert 氏 (Paderborn University)
Chevalley's restriction theorem for supersymmetric Riemannian symmetric spaces
[ 講演概要 ]
We start by explaining the concept of a supersymmetric Riemannian symmetric spaces and present the examples studied by Zirnbauer in the context of universality classes of random matrices. For these classes we then show how to formulate and prove an analog of Chevalley's restriction theorem for invariant super-functions.
This is joint work with A. Alldridge (Paderborn) and M. Zirnbauer (Cologne)
[ 参考URL ]We start by explaining the concept of a supersymmetric Riemannian symmetric spaces and present the examples studied by Zirnbauer in the context of universality classes of random matrices. For these classes we then show how to formulate and prove an analog of Chevalley's restriction theorem for invariant super-functions.
This is joint work with A. Alldridge (Paderborn) and M. Zirnbauer (Cologne)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html