## Geometry and Representation Theory Seminar

### Monday, March 18th, 2019

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

**Speaker:** Colin Ingalls (Carleton University)

**Title:** McKay quivers

**Abstract: ** Fix a finite group G and a representation W, the McKay quiver has vertices given by irreducible representations $V_i$ and $\dim\mathrm{Hom}_G(W\otimes V_i,V_j)$ many arrows between $V_i$ and $V_j$. We briefly present the history of McKay quivers and their applications in geometry and representation theory. Then we discuss recent descriptions of McKay quivers of relfection groups by M. Lewis, and work with E. Faber and R. Buchweitz applying results of Lustzig on McKay quivers to understand the relations of the basic model of the skew group ring.