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Journal Articles Annales de l'Institut Fourier Year : 2021

Braid groups of normalizers of reflection subgroups

Abstract

Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case.

Dates and versions

hal-02481266 , version 1 (17-02-2020)

Identifiers

Cite

Thomas Gobet, Anthony Henderson, Ivan Marin. Braid groups of normalizers of reflection subgroups. Annales de l'Institut Fourier, 2021, 71 (6), pp.2273-2304. ⟨10.5802/aif.3440⟩. ⟨hal-02481266⟩
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