Constructing Braided Tensor Categories Related to the Singlet and Simple Affine Vertex Algebras of sl(3)

Matthew Rupert (Logan, UT)

Abstract

The Kazhdan-Lusztig correspondence is a series of (usually conjectural) equivalences between categories of modules for quantum groups and vertex operator algebras. In this talk I will give an overview of the history of the Kazhdan-Lusztig correspondence and discuss some recent results related to these conjectures with a focus on the singlet and simple affine vertex algebras of sl(3).