Masaki Mori, Winter School on Representation Theory of Real Reductive Groups, Shunsuke Tsuchioka, Ivan Cherednik, Masaki Watanabe, Pablo Ramacher #1, Pablo Ramacher #2, Gordan Savin, Representation Theory and Group Actions on the occasion of the award of Purple Ribbon to Professor Kobayashi, Patrick Delorme,

Date: | January 14 (Tue), 2014, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Masaki Mori (森真樹) (the University of Tokyo) |

Title: | A cellular classification of simple modules of the Hecke-Clifford superalgebra |

Abstract: [ pdf ] |
The Hecke-Clifford superalgebra is a super version of the Iwahori-Hecke algebra of type A. Its simple modules are classified by Brundan, Kleshchev and Tsuchioka using a method of categorification of affine Lie algebras. However their constructions are too abstract to study in practice. In this talk, we introduce a more concrete way to produce its simple modules with a generalized theory of cellular algebras which is originally developed by Graham and Lehrer. In our construction the key is that there is a right action of the Clifford superalgebra on the super-analogue of the Specht module. With the help of the notion of the Morita context, a simple module of the Hecke-Clifford superalgebra is made from that of the Clifford superalgebra. |

Winter School on Representation Theory of Real Reductive GroupsGraduate School of Mathematical Sciences, the University of Tokyo | |

February 15 (Sat), Room 122 | |

13:00-14:00 | L. Barchini Invariants attached to Harish-Chandra modules. I. |

14:30-15:30 | F. Januszewski Algebraic Characters of Harish-Chandra modules and applications to branching problems 1. Motivation and general definition |

16:30-17:30 | T. Kobayashi Real spherical manifolds, symmetry breaking operators, and Shintani functions |

February 16 (Sun), Room 122 | |

13:00-14:00 | L. Barchini Invariants attached to Harish-Chandra modules. II |

14:30-15:30 | T. Kubo The Dynkin index and parabolic subalgebras of Heisenberg type |

16:30-17:30 | F. Januszewski Algebraic Characters of Harish-Chandra modules and applications to branching problems. 2. fundamental properties of algebraic characters |

February 17 (Mon), Room 122 | |

9:00-10:00 | H. Matumoto Homomorphisms between scalar generalized Verma modules (SGVM) with regular infinitesimal characters |

10:30-11:30 | F. Januszewski Algebraic Characters of Harish-Chandra modules and applications to branching problems. 3. applications to branching problems |

February 18 (Tue), Room 126 | |

10:00-11:00 | T. Kobayashi Discretely decomposable restrictions |

11:30-12:30 | L. Barchini Invariants attached to Harish-Chandra modules. III |

Organizers: T. Kobayashi, T. Kubo, H. Matumoro, H. Sekiguchi | |

Date: | April 15 (Tue), 2014, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Shunsuke Tsuchioka (土岡俊介) (the University of Tokyo) |

Title: | Toward the graded Cartan invariants of the symmetric groups |

Abstract: [ pdf ] |
We propose a graded analog of Hill's conjecture which is equivalent to K\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups. We give justifications for it and discuss implications between the variants. Some materials are based on the joint work with Anton Evseev. |

Date: | May 13 (Tue), 2014, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Ivan Cherednik (The University of North Carolina at Chapel Hill, RIMS) |

Title: | Global q,t-hypergeometric and q-Whittaker functions |

Abstract: [ pdf ] |
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior. The definition of the global functions was suggested about 14 years ago; it is conceptually different from the definition Heine gave in 1846, which remained unchanged and unchallenged since then. Algebraically, the new functions are closer to Bessel functions than to the classical hypergeometric and Whittaker functions. The analytic theory of these functions was completed only recently (the speaker and Jasper Stokman). The construction is based on DAHA. The global functions are defined as reproducing kernels of Fourier-DAHA transforms. Their specializations are Macdonald polynomials, which is a powerful generalization of the Shintani and Casselman-Shalika p-adic formulas. If time permits, the connection of the Harish-Chandra theory of global q-Whittaker functions will be discussed with the Givental-Lee formula (Gromov-Witten invariants of fl ag varieties) and its generalizations due to Braverman and Finkelberg (algebraic theory of affine flag varieties). |

Date: | May 27 (Tue), 2014, 17:00-18:30 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Masaki Watanabe (渡部正樹) (The University of Tokyo) |

Title: | Schubert加群の構造とSchubert加群によるfiltrationについて |

Abstract: [ pdf ] |
Schubert多項式を研究する道具の1つとして, KraskiewiczとPragaczによって導入されたSchubert加群があります. 今回の発表では, Schubert加群の構造に関する新しい結果と, そこから得られ る, 与えられた加群がSchubert加群によるfiltrationを持つ条件について話しま す. また, この研究のもともとの動機はSchubert多項式に関するある問題を考えてい たことなので, それについても話す予定です. |

Date: | June 17 (Tue), 2014, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Pablo Ramacher (Marburg University) |

Title: | Singular equivariant asymptotics and the momentum map. Residue formulae in equivariant cohomology. |

Abstract: [ pdf ] |
Let M be a smooth manifold and G a compact connected Lie group acting on M by isometries. In this talk, we study the equivariant cohomology of the cotangent bundle of M, and relate it to the cohomology of the Marsden-Weinstein reduced space via certain residue formulae. In case of compact symplectic manifolds with a Hamiltonian G-action, similar residue formulae were derived by Jeffrey, Kirwan et al. |

Date: | July 1 (Tue), 2014, 16:30-18:00 |

Place: | Room 126, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Pablo Ramacher (Marburg University) |

Title: | WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS |

Abstract: [ pdf ] |
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. |

Date: | July 3 (Thu), 2014, 16:00-18:00 |

Place: | Room 470, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Gordan Savin (The University of Utah) |

Title: | Structure of rational orbits in prehomogeneous spaces |

Abstract: [ pdf ] |
A prehomogeneous space is an algebraic representation of a reductive group that has a Zariski open orbit. Classifying orbits over a general field (or even a ring) is a non-trivial problem. A typical example is GL(n) acting on the space of symmetric matrices. In this case the orbits are classified by the isomorphism classes of quadratic spaces. In this lecture I will give a detailed exposition of a case related to a work of Bhargava. |

Representation Theory and Group Actions on the occasion of the award of Purple Ribbon to Professor Kobayashi | |

Date: | July 12 (Sat), 2014, 9:30-17:00 |

Place: | Graduate School of Mathematical Sciences, the University of Tokyo (Komaba) |

Program: |
Toshio Oshima (Josai University) (9:30-10:30)Hypergeometric systems and Kac-Moody root systems |

Godan Savin (University of Utah) (10:45-11:45)Representations of covering groups with multiplicity free K-types. | |

Mikhail Kapranov (Kavli IPMU) (13:20-14:20) Perverse sheaves on hyperplane arrangements | |

Masaki Kashiwara (RIMS) (14:40-15:40)Upper global nasis, cluster algebra and simplicity of tensor products of simple modules | |

Toshiyuki Kobayashi (the University of Tokyo, Kavli IMPU) (16:00-17:00)Branching Problems of Representations of Real Reductive Groups | |

Abstract: | [ pdf ] |

Date: | October 29 (Wed), 2014, 16:30-18:00 |

Place: | Room 118, Graduate School of Mathematical Sciences, the University of Tokyo |

Speaker: | Patrick Delorme (UER Scientifique de Luminy Université d'Aix-Marseille II) |

Title: | Harmonic analysis on reductive p-adic symmetric spaces |

Abstract: [ pdf ] |
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. |

© Toshiyuki Kobayashi