University of Sydney Algebra Seminar

Ivan Marin (Universite d'Amiens)

Friday 8 March, 12-1pm, Place: Carslaw 375

New algebras associated to reflection groups

A number of algebraic constructions have been extended from the symmetric groups to other reflection groups. The Coxeter theory has been the source of most of them, notably for the definition of the Hecke algebras, in the case of real reflection groups. Generalizations of these Hecke algebras to non-real ones have been proposed 20 years ago, using topological means (braid groups and monodromy representations). The properties of these generalizations were partly conjectural, and the main conjecture in this area has been resolved only recently. After having reviewed the corresponding material, we shall describe new extensions of these Hecke algebras which make sense in this general setting, as well as generalizations of the algebra of Brauer diagrams. Altogether, this provides large algebras associated to reflection groups whose structure and combinatorics still has to be determined.