Representations of braid groups of Lie type

John J. Millson

Knots in Washington XVI; Conference on Knot Theory and its Ramifications
May 5-7, 2003
University of Maryland
College Park, MD, USA

Organizers
Marta M. Asaeda (UMD), William M. Goldman (UMD), John J. Millson (UMD), Jozef H. Przytycki (GWU)

Conference Homepage

Representations of braid groups of Lie type
by
John J. Millson
University of Maryland
Coauthors: Valerio Toledano Laredo

I will discuss recent joint work with Toledano Laredo on the monodromy of the Casimir connection. The monodromy representation of this connection leads to a functor from representations V of a simple complex Lie algebra g to representations of the corresponding braid group of Lie type Bg ( on the zero weight space V[0] of V). I will discuss the problem of when this braid group representation is reducible answering a question of Procesi and Knutson. I will also give counterexamples using the same idea to a related conjecture of Kwon and Lusztig on representations of Bg coming from the quantum group associated to g.

Date received: April 28, 2003