| Date: | May 7 (Tue), 1997, 16:30-18:00 |
| Place: | Room 122, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Kenji Taniguchi (谷口健二) (University of Tokyo) |
| Title: | Commutants of r -2-type Hamiltonian |
| Abstract: | r -2 型のポテンシャルを持つハミルトニアンと可換な微分作用素の族について、現在までに知られていることを概説する。 特にポテンシャル関数が有理関数の場合に、Dunkl 作用素を用いて sl(2) の oscillator 表現の類似物を作ることによりこの族(の一部分)を自然 に構成する。 Weyl 群不変な可換微分作用素系の２階の作用素(Laplacian)と可換な作用素はこの系に含まれるか、という問題について論じる。 |
| Date: | May 13 (Tue), 1997, 16:30-18:00 |
| Place: | Room 122, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Takahiro Hayata (早田孝博) (University of Tokyo) |
| Title: | 対称対 (SU(2,2), Sp(2,R)) の新谷関数 |
| Abstract: | $G$ を半単純リー群, $\pi$ をその admissible 表現, ある involution で固定される部分群 $H$ とそのユニタリ表現を $\eta$ としたとき, $\rom{Hom}\,(\pi, C_{\eta}^{\infty}(H\backslash G))$ あるいは, $K$ 有限ベクトルのそれによる像を ここでは, 対称対 $(G,H)$ の新谷関数と呼んでいる. $\eta$ が単位表現の時には, Flensted-Jensen による結果がある が, ここでは, $(G,H)$ がタイトルの対称対のとき, $\eta$ とし て正則離散系列をとった場合の計算を紹介したい. |
| (Survey seminar) | |
| Date: | May 20 (Tue), 1997, 16:30-18:00 |
| Place: | Room 122, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Hisayosi Matumoto (松本久義) (University of Tokyo) |
| Title: | Howe duality の解説 (noncompact case) |
| Abstract: | 実数体上の reductive dual pair についての Howe duality を最も一般的な 状況のおいて確立した、R. Howe の論文 Transcending classical invariant theory, J. of Amer. Math. Soc. 2 (1989), 535-552. の紹介を する。昨年の整数論サマースクールでのべれなかった、主定理の証明の方針に ついて主に解説する予定である。 |
| (Joint seminar of Geometry Colloquium-Lie Groups and Representation Theory Seminar) | |
| Date: | May 22 (Thu), 1997, 16:30-18:30 |
| Place: | Room 128, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Toshiyuki Kobayashi (小林俊行) (University of Tokyo) |
| Title: | 擬リーマン等質多様体における不連続群と変形 |
| Abstract: |
つぎの２つの話題を紹介する予定です：
一方，既約リーマン対称空間のコンパクトなクリフォード=クライン形で連続変形できるのは，２次元，すなわち閉リーマン面の場合に限る（Selberg-Weil の古典的な局所剛性定理）が，擬リーマン計量をもつ場合は高次元でも連続変形できる例が存在することがわかった．(1) の判定条件を援用して, 局所変形の量的評価を与える． 特に，３次元定曲率ローレンツ多様体における Goldman の提起した問題と予想（1985）の（高次元での一般化を含めた）定式化とその証明を与える． |
| Date: | May 27 (Tue), 1997, 16:30-18:00 |
| Place: | Room 122, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Tibor Ódor (University of Tokyo & University of Szeged (Hungary); Mathematical Institute of the Hungarian Academy of Sciences) |
| Title: | On the Pompeiu problem and its equivalent forms |
| Abstract: | Let $f$ be a continuous function and let $\Omega$ be a bounded open domain with connected Lipschitzian boundary in the $d$ dimensional real vector space $R^d$ having the property that the integral of the function $f$ is zero on every congruent copy of the domain $\Omega$. If $f$ must be zero, then we say that the domain $\Omega$ has the Pompeiu property. The only known bounded open domains which fails to have the Pompeiu property are the balls. The longstanding conjecture of Raleigh, Pompeiu and Schiffer that there are no other $\Omega$'s failing the Pompeiu property. The problem has non trivial connections to Lie group representations, overdetermined Neumann problems and even to combinatorics. It has several equivalent forms. In the first part of the lecture we overview some of the most important results, and in the second part I would like to talk about my work on the problem. |
| Date: | June 3 (Tue), 1997, 16:30-18:00 |
| Speaker: | Soji Kaneyuki (金行壮二) (Sophia University) |
| Title: | パラエルミート対称空間の自己同型群 |
| Abstract: | A (simple) parahermitian symmetric space is a simple symmetric space which admits an invariant symplectic structure and a pair of invariant, completely integrable Lagrangian distributions. By the automorphism group of such a space, we mean the group of diffeomorphisms which leave the two Lagrangian distributions invariant. A fundamental problem is to determine the automorphism group for each simple parahermitian symmetric space. This was settled by Noburu Tanaka for classical parahermitian symmetric spaces. In this talk, by using graded Lie algebras, we solve the problem for arbitrary simple parahermitian symmetric spaces. |
| Date: | June 10 (Tue), 1997, 16:30-18:00 |
| Speaker: | Hiroshi Tamaru (田丸博士) (Sophia University) |
| Title: | Orbit types of s-representations and graded Lie algebras |
| Abstract: | 半単純対称空間の線形 isotropy 表現を s-representation と呼ぶ. S-representation の全ての局所的な軌道型, つまり全ての固定 部分群の Lie 環は, 対称空間の制限ルート系を用いて決定できる. また同様の方法によって, 各 Graded Lie 環のある２つの部分環も制限 ルート系のみから決定できる. |
| Date: | June 17 (Tue), 1997, 17:00-18:30 |
| Speaker: | Ian Grojnowski |
| Title: | Affine Hecke algebras and their representations |
| Abstract: | I will define the affine Hecke algebra associated to a reductive group G, and describe the parametrisation and dimensions of its irreducible representations, even at roots of unity. |
| Date: | June 24 (Tue), 1997, 17:00-18:30 |
| Speaker: | Toshihiko Matsuki (松木敏彦) (Kyoto University) |
| Title: | リー群の２つの involution に関する両側剰余類分解 (noncompact case) |
| Abstract: |
G を reductive リー群、H と L を G の対称部分群（G のある involution に
関する固定部分群の開部分群）とするとき、両側剰余類分解
|
| Date: | July 1 (Tue), 1997, 16:30-18:00 |
| Speaker: | Toshinori Oaku (大阿久俊則) (Yokohama City University) |
| Title: | Computing with D-modules using Groebner bases --- a user's guide to Kan |
| Abstract: | D-加群(線形偏微分方程式系)の理論では特性多様体、重複度、 b-関数(indicial polynomial)などの不変量や、制限、積分、テンソル積、 local cohomology などの種々の functor が定義され重要な役割を演じる。 従来これらを具体的に計算することは困難であったが、 近年微分作用素環における Groebner 基底を用いることによって、 これらのいくつかを計算するアルゴリズムが得られることがわかってきた。 Groebner 基底によって特性多様体、b-関数、制限などがどうやって 計算できるかを、理論的なアルゴリズムと、高山信毅氏によって作成された 数式処理システム Kan を用いた実際の計算法の両面から解説する。 |
| Date: | October 7 (Tue), 1997, 16:30-17:30 |
| Place: | Room 202, RIMS, Kyoto University |
| Speaker: | Eric Opdam |
| Title: | On the Knizhnik Zamolodchikov equations for complex reflection groups |
| Date: | October 9 (Thu), 1997, 16:30-17:30 |
| Place: | Room 102, RIMS, Kyoto University |
| Speaker: | Grigori Olshanski |
| Title: | Shifted Schur functions and their applications |
| Date: | October 14 (Tue), 1997, 16:30-17:30 |
| Place: | Room 202, RIMS, Kyoto University |
| Speaker: | Eric Opdam |
| Title: | Symmetries for fake degrees of complex reflection groups |
| Abstract: | The second talk is an application of the first, and in the first talk I can explain some topological results of Broue, Malle, and Rouquier for orbit spaces, and results/conjectures for Dunkl theory for complex reflection groups. |
| Date: | November 11 (Tue), 1997, 16:30-17:30 |
| Place: | Room 202, RIMS, Kyoto University |
| Speaker: | Grigori Olshanski |
| Title: | Applications of shifted symmetric functions in representation theory |
| Date: | November 13 (Thu), 1997, 16:30-17:30 |
| Place: | Room 102, RIMS, Kyoto University |
| Speaker: | Andreas Nilsson |
| Title: | Multipliers on symmetric spaces |
| Date: | November 25 (Tue), 1997, 16:30-17:30 |
| Place: | Room 202, RIMS, Kyoto University |
| Speaker: | Eric Opdam |
| Title: | Residue calculus for root systems |
| Date: | December 9 (Tue), 1997, 16:00-17:00 |
| Speaker: | Andreas Nilsson (RIMS) |
| Title: | Fourier multipliers on pseudo-Riemannian symmetric spaces |
| Abstract: | In this talk we will consider multipliers for K-invariant functions on non-Riemannian symmetric spaces. They seem to have similar behavior as the multipliers in the Riemannian case, even if only partial results are known so far. We will give sufficient and also in some cases necessary conditions for Lp-boundedness of the corresponding operators. |
| Date: | December 9 (Tue), 1997, 17:15-18:15 December 11 (Thu), 1997, 16:30-18:00 |
| Place: | Room 122, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Grigori Olshanski (RIMS, Kyoto Univ., and Dobrushin Math. Lab., IPIT, Moscow) |
| Title: | Distinguished central basis for enveloping algebras of classical type and Capelli identities (2 lectures) |
| Abstract: | Let $G$ be any of the complex classical groups $GL(n)$, $O(2n+1)$, $Sp(2n)$, $O(2n)$, and let $Z$ be the center of the corresponding universal enveloping algebra. The purpose of the talks is to discuss a distinguished linear basis in the algebra $Z$. This basis arises, in a natural way, from the binomial formula for $G$ (a Taylor--type expansion of finite--dimensional irreducible characters of $G$). The eigenvalues of the basis elements in irreducible $G$-modules are certain factorial Schur polynomials --- new combinatorial functions, discovered by Biedenharn and Louck and studied by Macdonald and other authors. One of the remarkable properties of the distinguished basis is its connection with generalized Capelli identities. |
| Date: | December 19 (Fri), 1997, 16:30-18:00 |
| Place: | Room 118, Graduate School of Mathematical Sciences, Komaba |
| Speaker: | Corrado Marastoni (University of Padova) |
| Title: | Integral transforms for sheaves and D-modules: Radon-Penrose correspondence, Grassmann duality and the action of real forms of SL_n(C) |
| Abstract: | after introducing the general framework of integral transforms in the language of sheaves and D-modules, I will concentrate on Grassmannians to study the Radon- Penrose p-plane correspondence (joint work with A. D'Agnolo) and the "Grassmann duality" (my recent Ph.D. thesis at Paris VI). The final aim is to examine the action of real forms of SL_n(C) on these transforms, and to discuss the links with representation theory. |
| Date: | January 26 (Mon)-28 (Wed), 1998, 14:40-16:10 |
| Speaker: | Toshiyuki Kobayashi (小林俊行) (University of Tokyo) |
| Title: | Unitary Highest Weight Modules and Multiplicity Free Branching Laws (3 lectures) |
| Abstract: |
|
| Date: | February 3 (Tue), 1998, 16:30-18:00 |
| Speaker: | Jean-Pierre Labesse (Centre International de Rencontres Mathématiques) |
| Title: | Selberg trace formula and index theorem |
| Abstract: | I compare the Selberg trace formula and the Index theorem; I show that both objects coincide for invariant elliptic operators on locally symetric manifolds (this is more or less well known) using that pseudo-coefficients are closely related to heat-kernels techniques. The point is that various generalizations and problems arise naturally: in particular this gives $L^2$ index theorems if the manifold is only of finite volume; moreover one can consider equivariant index formula that correspond to twisted trace formula and also to the action of Hecke operators explicit computation of the various terms that show up is not known in general but examples show that this contains in particular twisted characters formula and also eta-invariants etc... |
© Toshiyuki Kobayashi