On Some Monoids Associated to Coxeter Groups
Time and place
1 PM on Tuesday, September 20th, 2011; NAC 6-113
Prof. Stuart Margolis (Bar-Ilan University, Israel)
Abstract
Coxeter groups are one of the most ubiquitous objects in mathematics, arising in a number of different guises. In particular, associated with any Coxeter group W is its Coxeter complex C(W), the hyperplane arrangement arising from W's natural definition as a reflection group and a number of partial orders, the most important one being Bruhat order.
These geometric and combinatorial objects play a crucial role in the representation theory of W and other connections between W, geometry and algebraic combinatorics. In recent years it has been recognized that both C(W) and the Bruhat order have a natural structure of a monoid and that these monoids carry information about W, that the group structure alone can not see. We will define and explain the basic properties of these monoids and discuss their representation theory.
