Infinitesimal Hecke Algebras II

Details Infinitesimal Hecke Algebras II Infinitesimal Hecke Algebras II

2009-11-10

arxiv.org/abs/0911.1879v1

Mathematics

Representation Theory

Scientific paper

For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the group algebra of W by the reflections of W. We determine its decomposition in simple factors. In case W is a Coxeter group, we prove that the representations involved are unitarizable when the parameters of the representations have modulus 1 and are close to 1. We consequently determine the topological closure in this case.

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