Braid groups of normalizers of reflection subgroups

2020/02/13 by Gobet, Thomas, Henderson, Anthony, Marin, Ivan
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2002.05468

Abstract

Let W₀ be a reflection subgroup of a finite complex reflection group W, and let B₀ and B be their respective braid groups. In order to construct a Hecke algebra \widetildeH₀ for the normalizer N_W(W₀), one first considers a natural subquotient \widetildeB₀ of B which is an extension of N_W(W₀)/W₀ by B₀. We prove that this extension is split when W is a Coxeter group, and deduce a standard basis for the Hecke algebra \widetildeH₀. We also give classes of both split and non-split examples in the non-Coxeter case.

Related

• Infinitesimal Hecke Algebras II
• Lattice extensions of Hecke algebras
• The lattice of nil-Hecke algebras over real and complex reflection groups
• Infinitesimal Hecke Algebras IV
• Krammer representations for complex braid groups