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arXiv · 1710.03868

BMR freeness for icosahedral family

Shunsuke Tsuchioka
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Abstract

We verify the Brou\'e-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, Brou\'e-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.

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Shunsuke Tsuchioka. 2017-10-11. BMR freeness for icosahedral family. https://arxiv.org/abs/1710.03868

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