Speaker: Eirini Chavli (Paris)

Title: The BMR Freeness Conjecture: The Tetrahedral and Octahedral Families


In 1998 M. Broué, G. Malle and R. Rouquier conjectured that the generic Iwahori-Hecke algebra associated to a complex reflection group \(W\) is free of rank \(|W|\) as a module over its ring of definition \(R\). From recent work of I. Marin and G. Pfeiffer, the BMR conjecture is known to be true apart from 19 cases, the so-called exceptional groups of rank 2, and the case of a large complex reflection group, that hasn't been checked yet. The exceptional groups of rank 2 are divided into three families: the tetrahedral, octahedral and icosahedral family. In this talk, we will explain the method we used for proving the conjecture for the first two families, a method we are optimistic that can work in the case of the icosahedral family, as well (work in progress).