English

Infinitesimal Hecke Algebras III

Representation Theory 2010-12-21 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1012.4424,
  title  = {Infinitesimal Hecke Algebras III},
  author = {Ivan Marin},
  journal= {arXiv preprint arXiv:1012.4424},
  year   = {2010}
}
R2 v1 2026-06-21T17:01:51.156Z