The BMR freeness conjecture for the first two families of the exceptional groups of rank 2

Abstract

The freeness conjecture of Broué, Malle and Rouquier for the generic Hecke algebras associated with complex reflection groups is still open for 14 cases, which cover almost all the exceptional complex reflection groups of rank 2. We prove this conjecture for 9 of these remaining cases, giving a basis similar to the classical case of the finite Coxeter groups.