Lie Groups and Representation Theory

Seminar information archive ~07/20Next seminarFuture seminars 07/21~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2014/07/12

13:20-17:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Mikhail Kapranov (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
[ Abstract ]
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.
Masaki Kashiwara (RIMS) 14:40-15:40
Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
[ Abstract ]
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.
Toshiyuki Kobayashi (the University of Tokyo) 16:00-17:00
Branching Problems of Representations of Real Reductive Groups (ENGLISH)
[ Abstract ]
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.