## Geometry and Representation Theory Seminar

### Monday, September 10th, 2018

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Charles Paquette (Queen's/RMC)

**Title:** A quiver construction of some subalgebras of asymptotic Hecke algebras

**Abstract: ** Lusztig defines an asymptotic Hecke algebra J from a Coxeter system (W,S). This is an algebra that is defined using the Kazhdan-Lusztig (KL) basis of the corresponding Hecke algebra of (W,S). Even though these KL bases are generally hard to understand, there is a two-sided cell C of W that gives rise to a nice subalgebra J_C of J having rich combinatorics and whose algebraic description does not use KL bases. We will see that J_C has a presentation using a quiver with relations, and this allows one to study the representation theory of J_C (and of J) from another perspective. Using quiver representations, we will see that the classification of simple modules, which falls into three categories (finite type, bounded type and unbounded type), can be characterized completely using the shape of the weighted graph G of (W,S).

This is joint work with I. Dimitrov, D. Wehlau and T. Xu.