On Brauer algebra simple modules over the complex field

Abstract

This paper gives two results on the simple modules for the Brauer algebra B n ( δ ) B_n(\delta ) over the complex field. First we describe the module structure of the restriction of all simple B n ( δ ) B_n(\delta ) -modules to B n − 1 ( δ ) B_{n-1}(\delta ) . Second we give a new geometrical interpretation of Ram and Wenzl’s construction of bases for “ δ \delta -permissible” simple modules.