##### Department of Mathematics,

University of California San Diego

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### University of California Lie Theory Workshop

## Tom Halverson

#### Macalester College

## \bf \huge $q-$Partition Algebras

##### Abstract:

The partition algebra is the centralizer of the symmetric group acting on tensor powers of its natural (permutation) module. It has a diagrammatic basis that generalizes Brauer's centralizer algebra for the orthogonal group. Many of these diagram centralizer algebras have q-generalizations: for example the q-symmetric group is the Iwahori-Hecke algebra and the q-Brauer algebra is the BMW algebra. We will introduce a candidate for a q-partition algebra --- constructed using Harish-Chandra restriction and induction on the finite general linear group over a field with q elements --- and we will illustrate some preliminary computations in this algebra.

Host: Efim Zelmanov

### February 17, 2008

### 3:10 PM

### NSB 1205

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