Whittaker Categories and Whittaker Modules for 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, the construction of Whittaker modules from Whittaker modules for the even part.

Key Words:

• Lie superalgebras
• Whittaker categories
• Whittaker modules

2010 Mathematics Subject Classification:

• 17B10

Notes

Communicated by K. Misra.