Category O Representations of the Lie Superalgebra osp(3,2)

Abstract

In his seminal 1977 paper [Kac77], V. G. Kac classified the finite dimensional simple Lie superalgebras over algebraically closed fields of characteristic zero. However, over thirty years later, the representation theory of these algebras is still not completely understood, nor is the structure of their enveloping algebras. In this thesis, we consider a low-dimensional example, osp(3,2). We compute the composition factors and Jantzen filtrations of Verma modules over osp(3,2) in a variety of cases.