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- W4301376520 abstract "In this paper we prove the existence of the Dunkl weight function $K_{c, lambda}$ for any irreducible representation $lambda$ of any finite Coxeter group $W$, generalizing previous results of Dunkl. In particular, $K_{c, lambda}$ is a family of tempered distributions on the real reflection representation of $W$ taking values in $text{End}_mathbb{C}(lambda)$, with holomorphic dependence on the complex multi-parameter $c$. When the parameter $c$ is real, the distribution $K_{c, lambda}$ provides an integral formula for Cherednik's Gaussian inner product $gamma_{c, lambda}$ on the Verma module $Delta_c(lambda)$ for the rational Cherednik algebra $H_c(W, mathfrak{h})$. In this case, the restriction of $K_{c, lambda}$ to the hyperplane arrangement complement $mathfrak{h}_{mathbb{R}, reg}$ is given by integration against an analytic function whose values can be interpreted as braid group invariant Hermitian forms on $KZ(Delta_c(lambda))$, where $KZ$ denotes the Knizhnik-Zamolodchikov functor introduced by Ginzburg-Guay-Opdam-Rouquier. This provides a concrete connection between invariant Hermitian forms on representations of rational Cherednik algebras and invariant Hermitian forms on representations of Iwahori-Hecke algebras, and we exploit this connection to show that the $KZ$ functor preserves signatures, and in particular unitarizability, in an appropriate sense." @default.
- W4301376520 created "2022-10-05" @default.
- W4301376520 creator A5021182619 @default.
- W4301376520 date "2018-03-01" @default.
- W4301376520 modified "2023-09-23" @default.
- W4301376520 title "The Dunkl Weight Function for Rational Cherednik Algebras" @default.
- W4301376520 doi "https://doi.org/10.48550/arxiv.1803.00440" @default.
- W4301376520 hasPublicationYear "2018" @default.
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