Lie群論・表現論セミナー

過去の記録 ~05/21次回の予定今後の予定 05/22~

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 http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

過去の記録

2018年03月12日(月)

15:00-16:30   数理科学研究科棟(駒場) 126号室
Christian Ikenmeyer 氏 (Max-Planck-Institut fur Informatik)
Plethysms and Kronecker coefficients in geometric complexity theory
[ 講演概要 ]
Research on Kronecker coefficients and plethysms gained significant momentum when the topics were connected with geometric complexity theory, an approach towards computational complexity lower bounds via algebraic geometry and representation theory. This talk is about several recent results that were obtained with geometric complexity theory as motivation, namely the NP-hardness of deciding the positivity of Kronecker coefficients and an inequality between rectangular Kronecker coefficients and plethysm coefficients. While the proof of the former statement is mainly combinatorial, the proof of the latter statement interestingly uses insights from algebraic complexity theory. As far as we know algebraic complexity theory has never been used before to prove an inequality between representation theoretic multiplicities.

2017年10月24日(火)

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30, トポロジー火曜セミナーと合同
宮岡礼子 氏 (東北大学)
ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
[ 講演概要 ]
球面の等径超曲面のガウス写像による像は,複素2次超曲面Q_n(C)の極小ラグランジュ部分多様体の豊富な例を与える.簡単な場合,これはQ_n(C)の実形となり,そのフレアホモロジーは既知である.ここでは相異なる主曲率の個数が3,4,6の場合に得られた結果を報告するとともに,これらがFOOOの議論から直接得られるものではないことを述べる.当研究は,入江博(茨城大),Hui Ma(清華大学),大仁田義裕(大阪市大)との共同研究である.

2017年09月26日(火)

17:00-18:30   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
関口英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (Japanese)
[ 講演概要 ]
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.

I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.

To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.

Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.

2017年03月10日(金)

17:00-18:30   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.場所がいつもと異なりますので,ご注意ください.
Lizhen Ji 氏 (University of Michigan, USA)
Satake compactifications and metric Schottky problems (English)
[ 講演概要 ]
The quotient of the Poincare upper half plane by the modular group SL(2, Z) is a basic locally symmetric space and also the moduli space of compact Riemann surfaces of genus 1, and it admits two important classes of generalization:

(1) Moduli spaces M_g of compact Riemann surfaces of genus g>1,

(2) Arithmetic locally symmetric spaces \Gamma \ G/K such as the Siegel modular variety A_g, which is also the moduli of principally polarized abelian varieties of dimension g.

There have been a lot of fruitful work to explore the similarity between these two classes of spaces, and there is also a direct interaction between them through the Jacobian (or period) map J: M_g --> A_g.
In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective.

2016年07月05日(火)

17:00-18:00   数理科学研究科棟(駒場) 128号室
服部 俊昭 氏 (東工大・理・数学)
清水の補題の一般化について
[ 講演概要 ]
SL(n,C)のあるタイプの冪等元を含む部分群が離散部分群になるための必要条件を与える不等式が、n=2の場合(もともとの清水の補題の場合に相当)を拡張する形で得られることと、対応する対称空間へのその群の作用が不等式によって影響を受けることについて去年7月のこのセミナーでお話しいたしました。これはその後の進展の報告です。

2016年04月12日(火)

17:00-18:30   数理科学研究科棟(駒場) 128号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
Universal Gysin formulas for flag bundles
[ 講演概要 ]
We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

2015年11月26日(木)

17:00-18:45   数理科学研究科棟(駒場) 号室
Birgit Speh 氏 (Cornell University)
Introduction to the cohomology of discrete groups and modular symbols 2 (English)
[ 講演概要 ]
The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.

The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.


On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.


In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.

2015年11月24日(火)

17:00-18:45   数理科学研究科棟(駒場) 号室
Birgit Speh 氏 (Cornell University)
Introduction to the cohomology of discrete groups and modular symbols 1 (English)
[ 講演概要 ]
The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.

The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.


On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.


In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.

2015年07月28日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
Fabian Januszewski 氏 (Karlsruhe Institute of Technology)
On g,K-modules over arbitrary fields and applications to special values of L-functions
[ 講演概要 ]
I will introduce g,K-modules over arbitrary fields of characteristic 0 and discuss their fundamental properties and constructions, including Zuckerman functors. This may be applied to produce models of certain standard modules over number fields, which has applications to special values of automorphic L-functions, and also furnishes the space of regular algebraic cusp forms of GL(n) with a natural global Q-structure.

2015年07月21日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (Penn State University)
GEOMETRIC STRUCTURE IN SMOOTH DUAL
[ 講演概要 ]
Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F) , Sp(2n, F) , PGL(n, F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. This talk will first review the theory of the Bernstein center. According to this theory, the smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will then explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component.

The ABPS conjecture has been proved for GL(n, F), SO(n, F), and Sp(2n, F).

2015年07月21日(火)

15:30-16:30   数理科学研究科棟(駒場) 122号室
服部俊昭 氏 (東京工業大学)
清水の補題のSL(3,R)/SO(3)の場合への拡張について (Japanese)
[ 講演概要 ]
PSL(2,C)の部分群の離散性に関する必要条件である清水の補題,Jorgensenの不等式を双曲空間から他の階数1の対称空間の場合に拡張しようという研究が現在進行中であるが, 高階の対称空間についてそのような結果はまだないようである。階数が2の対称空間で最も簡単なSL(3,R)/SO(3)の場合に清水の補題を拡張する試みについてお話しする。

2015年07月14日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (Penn State University)
MORITA EQUIVALENCE REVISITED
[ 講演概要 ]
Let X be a complex affine variety and k its coordinate algebra. A k- algebra is an algebra A over the complex numbers which is a k-module (with an evident compatibility between the algebra structure of A and the k-module structure of A). A is not required to have a unit. A k-algebra A is of finite type if as a k-module A is finitely generated. This talk will review Morita equivalence for k-algebras and will then introduce --- for finite type k-algebras ---a weakening of Morita equivalence called geometric equivalence. The new equivalence relation preserves the primitive ideal space (i.e. the set of isomorphism classes of irreducible A-modules) and the periodic cyclic homology of A. However, the new equivalence relation permits a tearing apart of strata in the primitive ideal space which is not allowed by Morita equivalence.

Let G be a connected split reductive p-adic group, The ABPS (Aubert- Baum-Plymen-Solleveld) conjecture states that the finite type algebra which Bernstein assigns to any given Bernstein component in the smooth dual of G, is geometrically equivalent to the coordinate algebra of the associated extended quotient. The second talk will give an exposition of the ABPS conjecture.

2015年06月30日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
Anatoly Vershik 氏 (St. Petersburg Department of Steklov Institute of Mathematics)
Random subgroups and representation theory
[ 講演概要 ]
The following problem had been appeared independently in different teams and various reason:
to describe the Borel measures on the lattice of all subgroups of given group, which are invariant with respect to the action of the group by conjugacy. The main interest of course represents nonatomic measures which exist not for any group.
I will explain how these measures connected with characters and representations of the group, and describe the complete list of such measures for infinite symmetric group.

2015年05月26日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
小木曽岳義 氏 (城西大学)
Clifford quartic forms の局所関数等式とhomaloidal EKP-polynomials
[ 講演概要 ]
局所関数等式が正則概均質ベクトル空間の基本相対不変式とその双対空間の多項式のペアから与えられることは知られている。我々は Clifford quartic form と呼ばれるある4次斉次多項式を構成し, それが概均質ベクトル空間の相対不変式ではないにも関わらず局所関数等式を満たすことを示した。局所関数等式を満たす多項式を特徴付ける問題は興味深い未解決問題であるが, この問題に関連し、 Etingof, Kazhdan, Polishchuk は(もっと一般的な設定で)ある予想を提示した。我々は、 Clifford quartic form を用いて, この予想に反例があることを示した。 (この講演は佐藤文広氏との共同研究に基づいている。)

2015年05月19日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
Anton Evseev 氏 (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
[ 講演概要 ]
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.

2015年04月28日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
Bent Orsted 氏 (Aarhus University and the University of Tokyo)
Restricting automorphic forms to geodesic cycles (English)
[ 講演概要 ]
We find estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles in terms of their expansion into eigenfunctions of the Laplacian. Our method resembles earlier work on products of automorphic forms by Bernstein and Reznikov, and it uses Kobayashi's new symmetry-breaking kernels. This is joint work with Jan M\"o{}llers.

2015年04月21日(火)

17:00-18:30   数理科学研究科棟(駒場) 122号室
中濱 良祐 氏 (東京大学大学院数理科学研究科)
ベクトル値正則離散系列表現のノルム計算と解析接続 (English)
[ 講演概要 ]
正則離散系列表現は,複素有界対称領域上のベクトル値正則関数空間上に実現される.そのノルムはパラメータが十分大きい場合には収束する積分で表せるが,パラメータが小さくなるとその積分は収束しなくなる.しかし,ノルムを具体的に計算することによって,その小さいパラメータへの解析接続を考えることができ,そのユニタリ化可能性などの性質を論じることができる.本講演ではノルムの具体的な計算に関する結果を扱う.

2015年04月14日(火)

16:30-18:00   数理科学研究科棟(駒場) 122号室
田中 雄一郎 氏 (九州大学マス・フォア・インダストリ研究所)
複素球多様体へのコンパクトリー群の可視的作用について (English)
[ 講演概要 ]
With the aim of uniform treatment of multiplicity-free representations of Lie groups, T. Kobayashi introduced the theory of visible actions on complex manifolds.

In this talk we consider visible actions of a compact real form U of a connected complex reductive algebraic group G on G-spherical varieties. Here a complex G-variety X is said to be spherical if a Borel subgroup of G has an open orbit on X. The sphericity implies the multiplicity-freeness property of the space of polynomials on X. Our main result gives an abstract proof for the visibility of U-actions. As a corollary, we obtain an alternative proof for the visibility of U-actions on linear multiplicity-free spaces, which was earlier proved by A. Sasaki (2009, 2011), and the visibility of U-actions on generalized flag varieties, earlier proved by Kobayashi (2007) and T- (2013, 2014).

2015年04月07日(火)

16:30-18:00   数理科学研究科棟(駒場) 122号室
Bent Orsted 氏 (Aarhus University)
Branching laws and elliptic boundary value problems
(English)
[ 講演概要 ]
Classically the Poisson transform relates harmonic functions in the complex upper half plane to their boundary values on the real axis. In some recent work by Caffarelli et al. some new generalizations of this appears in connection with the fractional Laplacian. In this lecture we
shall explain how the symmetry-breaking operators introduced by T. Kobayashi for studying branching laws may shed new light on the situation for elliptic boundary value problems. This is based on joint work with J. M\"o{}llers and G. Zhang.

2015年03月24日(火)

18:00-19:30   数理科学研究科棟(駒場) 126号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
A Gysin formula for Hall-Littlewood polynomials
[ 講演概要 ]
Schubert calculus on Grassmannians is governed by Schur S-functions, the one on Lagrangian Grassmannians by Schur Q-functions. There were several attempts to give a unifying approach to both situations.
We propose to use Hall-Littlewood symmetric polynomials. They appeared implicitly in Hall's study of the combinatorial lattice structure of finite abelian p-groups and in Green's calculations of the characters of GL(n) over finite fields; they appeared explicitly in the work of Littlewood on some problems in representation theory.
With the projection in a Grassmann bundle, there is associated its Gysin map, induced by pushing forward cycles (topologists call it "integration along fibers").
We state and prove a Gysin formula for HL-polynomials in these bundles. We discuss its two specializations, giving better insights to previously known formulas for Schur S- and P-functions.

2015年01月27日(火)

16:30-18:00   数理科学研究科棟(駒場) 126号室
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
[ 講演概要 ]
Let $G$ be a connected simply connected simple complex algebraic group of type $ADE$ and $\mathfrak{g}$ the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of $U_q(\mathfrak{n}^+)$. Here, $U_q(\mathfrak{n}^+)$ denotes the positive part of the quantized enveloping algebra $U_q(\mathfrak{g})$. (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between $U_q(\mathfrak{n}^+)$ and the specific irreducible representations of the quantized function algebra $\mathbb{Q} _q[G]$. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right $U_q(\mathfrak{g})$-algebra structure of $\mathbb{Q}_q[G]$. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.

2014年10月29日(水)

16:30-18:00   数理科学研究科棟(駒場) 118号室
Patrick Delorme 氏 (UER Scientifique de Luminy Universite d'Aix-Marseille II)
Harmonic analysis on reductive p-adic symmetric spaces. (ENGLISH)
[ 講演概要 ]
In this lecture we will review the Plancherel formula that
we got by looking to neighborhoods at infinity of the
symmetric spaces and then using the method of Sakellaridis-Venkatesh
for spherical varieties for a split group. For us the group
is not necessarily split. We will try to show what questions
are raised by this work for real spherical varieties.
We will present in the last part a joint work with Pascale
Harinck and Yiannis Sakellaridis in which we prove Paley-Wiener
theorems for symmetric spaces.

2014年07月12日(土)

13:20-17:00   数理科学研究科棟(駒場) 126号室
Mikhail Kapranov 氏 (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
[ 講演概要 ]
Given an arrangement of hyperplanes in $R^n$, one has the complexified arrangement in $C^n$ and the corresponding category of perverse sheaves (smooth along the strata of the natural stratification).

The talk, based in a joint work with V. Schechtman, will present an explicit description of this category in terms of data associated to the face complex of the real arrangement. Such a description suggests a possibility of categorifying the concept of a oerverse sheaf in this and possibly in more general cases.
柏原正樹 氏 (京都大学数理解析研究所) 14:40-15:40
Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
[ 講演概要 ]
One of the motivation of cluster algebras introduced by
Fomin and Zelevinsky is
multiplicative properties of upper global basis.
In this talk, I explain their relations, related conjectures by Besrnard Leclerc and the recent progress by the speaker with Seok-Jin Kang, Myungho Kima and Sejin Oh.
小林俊行 氏 (東京大学大学院数理科学研究科) 16:00-17:00
Branching Problems of Representations of Real Reductive Groups (ENGLISH)
[ 講演概要 ]
Branching problems ask how irreducible representations π of groups G "decompose" when restricted to subgroups G'.
For real reductive groups, branching problems include various important special cases, however, it is notorious that "infinite multiplicities" and "continuous spectra" may well happen in general even if (G,G') are natural pairs such as symmetric pairs.

By using analysis on (real) spherical varieties, we give a necessary and sufficient condition on the pair of reductive groups for the multiplicities to be always finite (and also to be of uniformly bounded). Further, we discuss "discretely decomposable restrictions" which allows us to apply algebraic tools in branching problems. Some classification results will be also presented.

If time permits, I will discuss some applications of branching laws of Zuckerman's derived functor modules to analysis on locally symmetric spaces with indefinite metric.

2014年07月12日(土)

09:30-11:45   数理科学研究科棟(駒場) 126号室
大島利雄 氏 (城西大学) 09:30-10:30
超幾何系とKac-Moodyルート系 (ENGLISH)
[ 講演概要 ]
帯球関数やそれの一般化のHeckmann-Opdamの超幾何の解析のため,1次元
の特異集合への制限から常微分方程式の研究に興味を持った.
Fuchs型常微分方程式全体の空間にEuler変換などを通じてKac-Moodyルー
ト系のWeyl群が作用することが分かり,局所モノドロミーで決まらない
モジュライ空間の次元を不変量として,群軌道の有限性が明らかになった.
モジュライがないrigidな場合は自明な方程式に変換されるので具体的
解析が可能になり,逆にモジュライのある場合はPainleve方程式の構成
と分類への応用がある.これらは分岐のない不確定特異点も許す場合に
拡張されると共に,リジッドな場合は自然に多変数の超幾何への延長が
定義され,その解析に役立つ.古典的なAppellの超幾何などは後者に含
まれ,モノドロミーの可約性などがルート系の言葉で一般的に記述でき
る.これらの概説と共に,最近の結果や今後の問題ついて解説する.

Gordan Savin 氏 (the University of Utah) 10:45-11:45
Representations of covering groups with multiplicity free K-types (ENGLISH)
[ 講演概要 ]
Let g be a simple Lie algebra over complex numbers. McGovern has
described an ideal J in the enveloping algebra U such that U/J, considered as a g-module under the adjoint action, is a sum of all self-dual representations of g with multiplicity one. In a joint work with Loke, we prove that all (g,K)-modules annihilated by J have multiplicity free K-types, where K is defined by the Chevalley involution.

2014年07月01日(火)

16:30-18:00   数理科学研究科棟(駒場) 126号室
Pablo Ramacher
(Marburg University)
WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS (ENGLISH)
[ 講演概要 ]
Let G be a connected reductive complex algebraic group with split real form $G^\\sigma$.
In this talk, we introduce a distribution character for the regular representation of $G^\\sigma$ on the real locus of a strict wonderful G-variety X, showing that on a certain open subset of $G^\\sigma$ of transversal elements it is locally integrable, and given by a sum over fixed points.

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