Unitary representations of Hecke algebras of complex reflection groups

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 $\text{OO}$ 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}.