Classification of simple weight Virasoro modules with a finite-dimensional weight space

Details Classification of simple weight Virasoro modules with a finite-dimensional weight space Classification of simple weight Virasoro modules with a finite-dimensional weight space

2005-07-10

arxiv.org/abs/math/0507195v1

J. Algebra 307 (2007), no. 1, 209-214

Mathematics

Representation Theory

8 pages

Scientific paper

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a non-trivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either a simple highest or lowest weight module or a simple module from the intermediate series). This implies positive answers to two conjectures about simple pointed and simple mixed modules over the Virasoro algebra.

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