Unitary representations of Hecke algebras of complex reflection groups

Details Unitary representations of Hecke algebras of complex reflection groups Unitary representations of Hecke algebras of complex reflection groups

2009-10-05

arxiv.org/abs/0910.0680v1

Mathematics

Representation Theory

11 pages

Scientific paper

We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group $\mathfrak{S}_n$ over the complex numbers. Interestingly, the unitary representations in the category $\OO$ for the rational Cherednik algebra of type A studied in \cite{ESG} correspond to the unitary representations of the corresponding Hecke algebra via the KZ functor defined in \cite{GGOR}.

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