On Brauer algebra simple modules over the complex field

TL;DR

This paper investigates the structure of simple modules for the Brauer algebra over the complex numbers, providing a detailed restriction analysis and a new geometric interpretation of basis constructions.

Contribution

It offers a new geometric perspective on the basis construction for -permissible simple modules and describes the restriction structure of all simple modules.

Findings

Restriction structure of all simple modules described

New geometric interpretation of basis construction

Enhanced understanding of -permissible simple modules

Abstract

This paper gives two results on the simple modules for the Brauer algebra over the complex field. First we describe the module structure of the restriction of all simple modules. Second we give a new geometrical interpretation of Ram and Wenzl's construction of bases for the '\delta-permissible' simple modules.