On the representation theory of partial Brauer algebras

Abstract

In this paper we study the partial Brauer $\mathbb{C}$-algebras ${\mathfrak{R}}_n(\delta ,{\delta }^{\prime })$, where $n\in \mathbb{N}$ and $\delta ,{\delta }^{\prime }\in \mathbb{C}$. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction ${\mathfrak{R}}_{n-1}\hookrightarrow {\mathfrak{R}}_n$. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.

arXiv comment23 pages