# Representations of Birman-Murakami-Wenzl Algebras

Algebra/Geometry/Topology Seminar

#### by John Enyang

Institution: U. Melbourne
Date: Mon 16th November 2009
Time: 2:15 PM
Location: Sisalkraft Theatre, Architecture

Abstract: Let $W_n(q,r)$ denote the Birman-Murakami-Wenzl algebra over a field $\mathbb{F}$ and $S^\mu$ be a Specht module for $W_n(q,r)$. Then $S^\mu$ is equipped with a symmetric bilinear form $S^\mu\times S^\mu\to\mathbb{F}$, such that the quotient $D^\mu$ of $S^\mu$ by the radical of the form is either zero or absolutely irreducible. In this talk, we will suppose that $r$ is of the form $\pm q^k$, $k\in\mathbb{Z}$, where $q$ is not a root of unity, and provide an explicit basis for each non-zero $D^\mu$, together with a precise statement of the decomposition numbers of $W_n(q,r)$. Our construction will also allow us to discuss the restriction of the $W_n(q,r)$-modules $S^\mu$ and $D^\mu$ to $W_{n-1}(q,r)$.