Parabolic induction for modular finite W-algebras

Abstract: We give an overview of the theory of module of minimal dimension for reduced enveloping algebras of Lie algebras of reductive algebraic groups in positive characteristic. The focus will be on recent joint work with Topley and Westaway where we apply the theory of modular finite W-algebras to prove that large classes of minimal dimension modules are obtained by a process of parabolic induction. Specifically this covers the cases where the p-character lies in a unique sheet, and those where the minimal modules are invariant under twisting by the component group.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar