Algebra Seminar: Marin -- New algebras associated to reflection groups

Ivan Marin (Universite d’Amiens) 

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

Title: New algebras associated to reflection groups 

Abstract: 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.