Representation theory: from finite groups to supergroups

Date: Tuesday 8 November 2022

Abstract

We offer a certain perspective on representation theory with an eye toward motivating supergroups.  We will begin with a discussion of the more familiar case of finite groups, highlighting the importance of Sylow p-subgroups in their representation theory.  Then we will introduce supergroups, with an emphasis on examples, and explain how one can analogise the definition of Sylow subgroups to the super setting.  We finish with a recent theorem which describes explicit analogues of Sylow subgroups for the general linear and orthosymplectic supergroups.