##### Department of Mathematics,

University of California San Diego

****************************

### Algebra Seminar

## Hans Wenzl

#### UCSD

## Centralizer Algebras for Spinor Representations

##### Abstract:

Given a representation $V$ of a group $G$, it is a classical problem to determine the centralizer of its action on the n-th tensor power of $V$. If $V$ is the natural module of a classical Lie group, this led to the famous Schur-Weyl and Brauer-Weyl dualities. In this talk, we solve this problem for the spinor representation $S$. For even-dimensional Spin groups, the centralizer on the n-th tensor power of $S$ is given by a representation of $SO(n)$, with a similar result also for the odd-dimensional Spin groups. Time permitting, we discuss generalizations of this result to quantum groups and to classification of tensor categories. Please note: There will be a pre-talk for graduate students from 2:30 - 3:00. The regular talk will begin at 3:00.

### October 26, 2015

### 3:00 PM

### AP&M 7218

****************************