Whittaker categories and strongly typical Whittaker modules for Lie superalgebras

TL;DR

This paper extends the concept of Whittaker modules and categories from Lie algebras to Lie superalgebras, providing structural decompositions and characterizations of simple modules for classical types.

Contribution

It introduces Whittaker modules and categories for Lie superalgebras, including a decomposition theorem and a classification of strongly typical simple modules for type I superalgebras.

Findings

Decomposition of Whittaker categories based on sub-superalgebra actions

Description of strongly typical simple Whittaker modules for type I superalgebras

Extension of classical Lie algebra concepts to Lie superalgebras

Abstract

Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules.