The BMR freeness conjecture for the first two families of the exceptional groups of rank 2
type: Item
instance of: scholarly article
title: The BMR freeness conjecture for the first two families of the exceptional groups of rank 2
zbMATH Open document ID: 1361.20027
author: Eirini Chavli
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2017-01-10T00:00:00Z
review text: The freeness conjecture of \textit{M. Broué} et al. [J. Reine Angew. Math. 500, 127--190 (1998; Zbl 0921.20046)] (briefly BMR conjecture) states that the generic Hecke algebra for the complex reflection group \(W\) is free of finite rank. The BMR conjecture is still open for 14 cases, which cover almost all the exceptional complex reflection groups of rank 2. In this paper, the author proves the conjecture for 9 of these remaining cases, giving a basis similar to the classical case of the finite Coxeter groups. In particular, the main theorem (Theorem 5.1) states that the BMR conjecture holds for all the groups belonging to the tetrahedral and octahedral families.
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 6673216
zbMATH Keywords: Coxeter group
zbMATH Keywords: braid group
zbMATH Keywords: Hecke algebra
zbMATH Keywords: Broué-Malle-Rouquier freeness conjecture
MaRDI profile type: Publication
full work available at URL: j.crma.2016.11.016
OpenAlex ID: W2559895044
Wikidata QID: Q122961640
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DOI: 10.1016/J.CRMA.2016.11.016
description: scientific article; zbMATH DE number 6673216