Whittaker Modules over Generalized Virasoro Algebras

Abstract

In this article, we study Whittaker modules over generalized Virasoro algebras relative to some total order. We give the description of any Whittaker module and its Whittaker vectors. In particular, we determine all simple Whittaker modules, which provide the first known examples of simple nonweight modules over generalized Virasoro algebras. On the other hand, we also show that any Whittaker module over any generalized Virasoro algebra can be induced from a Whittaker module over some Virasoro subalgebra.

Key Words:

• Generalized Virasoro algebra
• Parabolic induction
• Whittaker module

2000 Mathematics Subject Classification:

• 17B10
• 17B65
• 17B68
• 17B70

ACKNOWLEDGMENT

The authors are grateful to the referee for valuable suggestions to improve the article. This work is partially supported by NSF of China (Grant 11026155).

Notes

Communicated by M. Bresar.