Whittaker Modules for Graded Lie Algebras

TL;DR

This paper introduces a classification of Whittaker modules for certain graded Lie algebras, establishing a correspondence with polynomial ring ideals, extending classical results to new algebraic structures.

Contribution

It defines Whittaker modules for graded Lie algebras and provides a classification framework linking modules to polynomial ring ideals, generalizing known results.

Findings

Bijective correspondence between Whittaker modules and polynomial ideals

Classification of simple Whittaker modules for graded Lie algebras

Application to concrete algebra examples

Abstract

In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. As a consequence of this, we obtain a classification of simple Whittaker modules for such algebras. Also, we study some concrete algebras as examples.