Whittaker Modules for the Virasoro Algebra

TL;DR

This paper extends the concept of Whittaker modules to the Virasoro algebra, providing classifications and structural results similar to those known for semisimple Lie algebras.

Contribution

It introduces the definition of Whittaker modules for the Virasoro algebra and establishes classification and composition series results.

Findings

Classification of simple Whittaker modules by central characters

Existence of composition series for general Whittaker modules

Analogues of classical results for semisimple Lie algebras

Abstract

Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.