|Date: Friday, September 25, 2015
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Weak order on finite Coxeter groups and representation theory of preprojective algebras
Abstract: Let W be a finite Coxeter group of simply-laced type. There is a natural edge-labeling of the Hasse diagram of weak order by join-irreducible elements of W which refines the labeling by positive roots (or equivalently reflecting hyperplanes). Let P be the preprojective algebra corresponding to W. (I will explain the definition of P.) Weak order on W also arises naturally in the representation theory of P, and there is a natural edge-labelling of the Hasse diagram of W by a class of representations of P called "layer modules". I will explain a bijection between join-irreducible elements of W and layer modules which transforms the first labeling of the Hasse diagram of W into the second. So far, the direction of application is primarily that we understand the representation theory of P better thanks to classical combinatorics of W, but I will also say some things about the way in which we hope that this construction will lead to new results about weak order on W. This is joint work with Osamu Iyama, Nathan Reading, and Idun Reiten.
Speaker: Hugh Thomas
Institution: University of Quebec at Montreal