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Unitary representations of Hecke algebras of complex reflection groups

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: 0910.0680
Source
arXiv
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Abstract

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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