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

Dong Liu; Shoulan Gao; Linsheng Zhu
November 2008
Journal of Mathematical Physics;Nov2008, Vol. 49 Issue 11, p113503
Academic Journal
In this paper, 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 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 a lowest weight module or an irreducible module of the intermediate series).


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