BMR freeness for icosahedral family

Shunsuke Tsuchioka

BMR freeness for icosahedral family

Representation Theory 2017-10-12 v1 Quantum Algebra

Authors: Shunsuke Tsuchioka

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.

Keywords

BMR freeness cyclotomic Hecke algebras complex reflection groups icosahedral family Bergman's diamond lemma

Cite

@article{arxiv.1710.03868,
  title  = {BMR freeness for icosahedral family},
  author = {Shunsuke Tsuchioka},
  journal= {arXiv preprint arXiv:1710.03868},
  year   = {2017}
}

Comments

14 pages

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