Bounded weight modules of the Lie algebra of vector fields on ${\mathbb{C}}^2$

Abstract

We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb{C}}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification we introduce a new family of generalized tensor $W_n$-modules. Our classification result is an important step in the classification of all simple weight $W_n$-modules with finite weight multiplicities.

arXiv comment24 pages, some corrections made

References in corpus (1)

• Category of sp(2n)-modules with bounded weight multiplicities

Cited by in corpus (1)

• Classification of simple bounded weight modules of the Lie algebra of vector fields on $\C^n$