# 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 *sl*_{2}(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.

## Recommended Citation

Wiesner, Emilie, "On the Representation Theory of the Virasoro Algebra" (2005). *Colloquia of the Department of Mathematical Sciences*. 190.

https://scholarworks.umt.edu/mathcolloquia/190

## Additional Details

Thursday, 17 March 2005

4:10 p.m. in Math 109