Proof of the BMR conjecture for G20 and G21

Abstract

We prove two new cases of the Broué-Malle-Rouquier freeness conjecture for the Hecke algebras associated to complex reflection groups. These two cases are the complex reflection groups of rank 2 called $G_{20}$ and $G_{21}$ in the Shephard and Todd classification. This reduces the number of remaining unproven cases to 3.