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

By Volodymyr Mazorchuk, Kaiming Zhao. 2005

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f693fad8eae75bba24860415ab9907d3ef542610

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In Algebra and Number Theory

1. Xiangqian Guo
2. R. Lu
3. Kaiming Zhao

In Geometry and Topology

1. Xiangqian Guo
2. R. Lu
3. Kaiming Zhao

In Statistical and Nonlinear Physics

1. Xiangqian Guo
2. R. Lu
3. Kaiming Zhao

Citations in the corpus

• Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra (2010, background): “For details, we refer readers to [22, 23, 25], the book [14] and references therein.”