Double affine Hecke algebras and Calogero-Moser spaces

In this paper we prove that the spherical subalgebra $e{H}_{1,\tau }e$ of the double affine Hecke algebra $H_{1,\tau }$ is an integral Cohen-Macaulay algebra isomorphic to the center $Z$ of $H_{1,\tau }$, and $H_{1,\tau }e$ is a Cohen-Macaulay $e{H}_{1,\tau }e$-module with the property $H_{1,\tau }=En{d}_{e{H}_{1,\tau }e}(H_{1,\tau }e)$. In the case of the root system $A_{n-1}$ the variety $Spec(Z)$ is smooth and coincides with the completion of the configuration space of the relativistic analog of the trigomonetric Calogero-Moser system. This implies the result of Cherednik that the module $e{H}_{1,\tau }$ is projective and all irreducible finite dimensional representations of $H_{1,\tau }$ are regular representation of the finite Hecke algebra.