University of Sydney Algebra Seminar

François Digne (Université de Picardie)

Friday 18th November, 12.05-12.55pm, Carslaw 157

Markov traces from representations of finite groups of Lie type

Markov traces are central functions on the braid groups, coming from the Hecke algebras of type A, which are used to get invariants of knots. They have been generalized to types B and D by Geck and Lambropoulou. Recent work by Y. Gomi shows that these traces can be computed using the character theory of finite groups of Lie type. This allows us to define Markov traces in a uniform way for any type of Weyl group, even for any type of Coxeter group and conjecturally for Hecke algebras associated to (some) complex reflection groups.