# 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.
Domain :

https://hal.archives-ouvertes.fr/hal-02481266
Contributor : Thomas Gobet <>
Submitted on : Monday, February 17, 2020 - 1:18:11 PM
Last modification on : Wednesday, February 19, 2020 - 1:10:05 PM

### Identifiers

• HAL Id : hal-02481266, version 1
• ARXIV : 2002.05468

### Citation

Thomas Gobet, Anthony Henderson, Ivan Marin. Braid groups of normalizers of reflection subgroups. 2020. ⟨hal-02481266⟩

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