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Infinitesimal Hecke algebras. (English. Abridged French version) Zbl 1056.20004
Summary: We define infinitesimal analogues of the Iwahori-Hecke algebras associated with finite Coxeter groups. These are reductive Lie algebras for which we announce several decomposition results. These decompositions yield irreducibility results for representations of the corresponding (pure) generalized braid groups deduced from Hecke algebra representations through tensor constructions.

MSC:
20C08 Hecke algebras and their representations
20F55 Reflection and Coxeter groups (group-theoretic aspects)
17B20 Simple, semisimple, reductive (super)algebras
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