Skip to content

Back to Departmental Colloquium: Spring 2001

Departmental Colloquium


Date: Thursday, Jan 18, 2001

Time: 4:15PM

Location: JWB 335


John J. Millson

University of Maryland

Title

Casimir operators and representations of generalized braid groups

Abstract

Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W. I will construct a one-parameter family of W -equivariant, unitary flat connections on h with values in any finite-dimensional g -module V and simple poles on the root hyperplanes. The fundamental group of the quotient by W of the complement of the root hyperplanes in h will be called the braid group of type g. The corresponding monodromy representation of the braid group of type g is a deformation of the action of (a finite extension of) W on V. I will discuss the resulting representations for the Cartan powers of the vector representation for the classical simple Lie algebras. This is a joint work with Valerio Toledano Laredo.

Representation Theory

Calendar file