Classification of irreducible weight modules with a finite dimensional weight space over twisted Heisenberg-Virasoro algebra

Details Classification of irreducible weight modules with a finite dimensional weight space over twisted Heisenberg-Virasoro algebra Classification of irreducible weight modules with a finite dimensional weight space over twisted Heisenberg-Virasoro algebra

2005-12-10

arxiv.org/abs/math/0512209v1

Mathematics

Representation Theory

LaTeX, 5 pages

Scientific paper

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, 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 twisted Heisenberg-Virasoro algebra, 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 from the intermediate series

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