BMR freeness for icosahedral family

Abstract

We verify the Broué-Malle-Rouquier (BMR) freeness for cyclotomic Hecke algebras associated with complex reflection groups $G_{17}$, $G_{18}$, $G_{19}$ in the Shephard-Todd classification. Together with results of Ariki, Ariki-Koike, Broué-Malle, Marin, Marin-Pfeiffer and Chavli, this settled affirmatively the BMR freeness conjecture. Our verification is inspired by Bergman's diamond lemma and requires 1GB memory and 5 days calculation on a PC.

arXiv comment14 pages