[ Seminar 2015  Past Seminars  Related conferences etc. ]
Place:  Usually Room 126 (this year) Graduate School of Mathematical Sciences, the University of Tokyo [ Access ] 
Date:  May 19 (Tue), 2015, 17:0018:30 
Place:  Room 122, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Anton Evseev (University of Birmingham) 
Title:  RoCK blocks, wreath products and KLR algebras 
Abstract: [ pdf ]  The socalled 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 ChuangKessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic KhovanovLaudaRouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of Rmatrices for modules over KLR algebras due to KangKashiwaraKim. 
Date:  May 26 (Tue), 2015, 17:0018:30 
Place:  Room 122, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Takeyoshi Kogiso (小木曽岳義) (Josai University) 
Title:  Local functional equations of Clifford quartic forms and homaloidal 
Abstract: [ pdf ] 
It is known that one can associate local functional equation to
the irreducible
relative invariant of an irreducible regular prehomogeneous vector
spaces.
We construct Clifford quartic forms that cannot obtained from
prehomogeneous
vector spaces, but, for which one can associate local functional
equations.
The characterization of polynomials which satisfy local functional
equations
is an interesting problem. In relation to this characterization
problem
(in a more general form), Etingof, Kazhdan and Polishchuk raised a
conjecture.
We make a counter example of this conjecture from Clifford quartic
forms.
(This is based on the joint work with F.Sato) 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 が（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。） 
Analytic Representation Theory of Lie Groups  
Date:  July 1 (Wed)July 4 (Sat), 2015 
Place:  Kavli IPMU, the University of Tokyo 
Speaker:  Masatoshi Kitagawa (Univ of Tokyo) 
Title:  On the irreducibility of U(g)^Hmodules 
Abstract: 
I will report on the irreducibility of U(g)^Hmodules arising from
branching problems.
It is wellknown that a U(g)^Kmodule Hom_K(W,V) is irreducible for any
irreducible (g, K)module V and Ktype W.
For a noncompact subgroup H, the same statement is not true in general.
In this talk, I will introduce a positive example and negative example
for the irreducibility of Hom_H(W,V).

Speaker:  Bent Ørsted (Aarhus University) 
Title:  Generalized Fourier transforms 
Abstract: 
In these lectures, based on joint work with Salem Ben Said and
Toshiyuki Kobayashi, we shall define a natural family of deformations
of the usual Fourier transform in Euclidian space. The main idea is
to replace the standard Laplace operator by a twoparameter family
of deformations in such a way, that it still is a member of a triple
generating the threedimensional simple Lie algebra. In particular
we shall describe

Speaker:  Anatoly Vershik (St. Petersburg State University) 
Title:  Cohomology with the coefficients in the unitary representations of the Lie groups and representations of current groups 
Abstract:  Accordingly to the old papers by H.Araki, (and related continuaion by VershikGelfandGraev in 70th) the nonlocal irreducible representations of the group of functions with values in Lie groups $G$ depends on the existence of the cocycles of this group with values in the unitary representation of it. Such cocycle do exist for $O(n,1)$ and $U(n,1)$ but not for the rest semsimple groups.We put the same question for Iwasawa subgroup $P$ of the groups of type $U(p,q)$ and $O(p,q)$ is it true that $H^1(P;\pi)\ne 0$, where $\pi$ is exact irreducible representation of $P$. This positive answer on this question allows to find out a nontrivial cohomology for nonunitary representations for semisimple groups and then to construct nonunitary representations of the corresponding current groups. 
© Toshiyuki Kobayashi