Whittaker Modules for Graded Lie Algebras

Understand

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.