Infinitesimal Hecke Algebras III

Details Infinitesimal Hecke Algebras III Infinitesimal Hecke Algebras III

2010-12-20

arxiv.org/abs/1012.4424v1

Mathematics

Representation Theory

Scientific paper

We define Lie subalgebras of the group algebra of a finite pseudo-reflection group that are involved in the definition of the Cherednik KZ-systems, and determine their structure. We provide applications for computing the Zariski closure of the image of generalized (pure) braid group B inside the representations of the corresponding Hecke algebras. We also get unitarizability results for the representations of B originating from Hecke algebras for suitable parameters, and relate our Lie algebras with the topological closure of B in these compact cases.

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