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

Yaohui Xue; Rencai Lü

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

Representation Theory 2020-01-14 v1

Authors: Yaohui Xue , Rencai Lü

Abstract

Let $W_n^+$ be the Lie algebra of the Lie algebra of vector fields on $\C^n$ . In this paper, we classify all simple bounded weight $W_n^+$ modules. Any such module is isomorphic to the simple quotient of a tensor module $F(P,M)=P\otimes M$ for a simple weight module $P$ over the Weyl algebra $K_n^+$ and a finite dimensional simple $\gl_n$ module $M$ .

Keywords

Lie algebra of vector fields simple bounded weight modules Weyl algebra tensor modules classification

Cite

@article{arxiv.2001.04204,
  title  = {Classification of simple bounded weight modules of the Lie algebra of vector fields on $\C^n$},
  author = {Yaohui Xue and Rencai Lü},
  journal= {arXiv preprint arXiv:2001.04204},
  year   = {2020}
}

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