Proof of the Broué–Malle–Rouquier Conjecture in Characteristic Zero (After I. Losev and I. Marin—G. Pfeiffer)

Abstract

We explain a proof of the Broué–Malle–Rouquier conjecture on Hecke algebras of complex reflection groups, stating that the Hecke algebra of a finite complex reflection group W is free of rank |W| over the algebra of parameters, over a field of characteristic zero. This is based on previous work of Losev, Marin– Pfeiffer, and Rains and the author. Keyword: Hecke algebra ; Complex reflection group ; Broué–Malle–Rouquier conjecture