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

By Dong Liu, Shoulan Gao, Linsheng Zhu. 2008

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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).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/48eebeecee1779e56bf40ef828cfcaff65a4490b