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

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

2008-01-17

arxiv.org/abs/0801.2603v2

published in J. Math. Phys. 49(11)(2008)

Mathematics

Representation Theory

10 pages

Scientific paper

10.1063/1.2996291

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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