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Abstract: For W a finite 2-reflection group and B its generalized braid group, wedetermine the Zariski closure of the image of B inside the correspondingIwahori-Hecke algebra. The Lie algebra of this closure is reductive andgenerated in the group algebra of W by the reflections of W. We determine itsdecomposition in simple factors. In case W is a Coxeter group, we prove thatthe representations involved are unitarizable when the parameters of therepresentations have modulus 1 and are close to 1. We consequently determinethe topological closure in this case.



Author: Ivan Marin

Source: https://arxiv.org/







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