The BMR freeness conjecture for the 2-reflection groups

We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections.Comment: 20 pages. Version 2 : the last remaining case (G34) of the conjecture for 2-reflection groups is now proved. Version 3 : additional details provided for the sample case of G2

The BMM symmetrising trace conjecture for the exceptional 2-reflection groups of rank 2

We prove the symmetrising trace conjecture of Brou\'e, Malle and Michel for the generic Hecke algebra associated to the exceptional irreducible complex reflection group $G_{13}$. Our result completes the proof of the conjecture for the exceptional 2-reflection groups of rank 2.Comment: 17 page