Primitive spectra of Lie superalgebras and Kac-Moody algebras

Abstract: 

The primitive spectrum of a reductive Lie algebra is a classical subject, studied by Dixmier, Duflo, Joseph, Vogan et al. It has been well-understood since the ‘80s and the theory has interesting connections to various aspects of representation theory of the Lie algebra, as well as to Kazhdan-Lusztig combinatorics. 

The primitive spectra of Lie superalgebras and Kac-Moody algebras behave rather differently. After a brief review of the classical case I will discuss recent progress on the super case, based on work in collaboration with V. Mazorchuk and I. Musson; and mention some preliminary results in the Kac-Moody case, in collaboration with V. Chari.