Bounded weight modules of the Lie algebra of vector fields on ${\mathbb   C}^2$
  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. 
Andrew Cavaness and Dimitar Grantcharov
math.RT