Bounded weight modules of the Lie algebra of vector fields on ℂ2

Abstract

We study weight modules of the Lie algebra [Formula: see text] of vector fields on [Formula: see text]. A classification of all simple weight modules of [Formula: see text] with a uniformly bounded set of weight multiplicities is provided. To achieve this classification, we introduce a new family of generalized tensor [Formula: see text]-modules. Our classification result is an important step in the classification of all simple weight [Formula: see text]-modules with finite weight multiplicities.