Lie Groups and Representation Theory

Seminar information archive ~11/29Next seminarFuture seminars 11/30~

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

2014/01/14

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Masaki Mori (the University of Tokyo)
A cellular classification of simple modules of the Hecke-Clifford
superalgebra (JAPANESE)
[ Abstract ]
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.