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arXiv · 0801.2603

Classification of irreducible weight modules over $W$-algebra W(2,2)

Dong Liu·Shoulan Gao·Linsheng Zhu
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Abstract

We show that the support of an irreducible weight module over the $W$-algebra $W(2, 2)$, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the the $W$-algebra $W(2, 2)$, having a nontrivial finite dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module of the intermediate series).

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BibTeXRIS

Dong Liu, Shoulan Gao, Linsheng Zhu. 2008-01-18. Classification of irreducible weight modules over $W$-algebra W(2,2). https://doi.org/10.1063/1.2996291

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