Eirini Chavli (Amiens)

The BMR freeness conjecture: recent work and open cases.

Abstract:

Between 1994 and 1998, the work of M. Broue, G. Malle, and R. Rouquier generalized in a natural way the definition of the Hecke algebra beyond a Coxeter group, for any finite arbitrary complex reflection group. Attempting to also generalize the properties of the Coxeter case, they stated a number of conjectures concerning the Hecke algebras. One specific example of importance regarding those yet unsolved conjectures is the so-called BMR freeness conjecture. This conjecture is proven to be true apart from 19 cases, known as the exceptional groups of rank 2. In this talk, we will explain the methods we used for proving the conjecture for 14 of these remaining cases and we will give some ideas to deal with the rest of them (work in progress).