On the Representation Theory of the Virasoro Algebra

Document Type

Presentation Abstract

Presentation Date

3-17-2005

Abstract

The Virasoro algebra is an interesting Lie algebra from a variety of perspectives. A common way to study Lie algebras is through their modules (or representations), that is, ways that the Lie algebra acts on vectors spaces.

I will give an introduction to the Virasoro algebra and its representation theory, comparing it to the classical Lie algebra sl2(ℂ). In particular, I will discuss simple modules L and Verma modules M, two fundamental types of modules, and their connections to blocks. My own research has focused on the Virasoro algebra module M⊕L. I'll present some of my results on the decomposition of this module by blocks and the potential connections to Hecke algebras and Kazhdan-Lusztig polynomials for the Viraso algebra, concepts which capture the geometric structure of blocks.

Additional Details

Thursday, 17 March 2005
4:10 p.m. in Math 109

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