---
abstract: 'In this paper we prove that the spherical subalgebra $eH_{1,\tau}e$ 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 $eH_{1,\tau}e$-module with the property $H_{1,\tau}=End_{eH_{1,\tau}e}(H_{1,\tau}e)$. 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 $eH_{1,\tau}$ is projective and all irreducible finite dimensional representations of $H_{1,\tau}$ are regular representation of the finite Hecke algebra.'
address: 'Department of Mathematics, MIT, 77, Massachusetts Ave., Cambridge, MA 02139, USA.'
author:
- Alexei Oblomkov
title: ' Double affine Hecke algebras and Calogero-Moser spaces'
---

Introduction {#introduction .unnumbered}
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Ivan Cherednik in his pioneering paper [@Ch3] introduced the double affine Hecke algebras. These algebras play a crucial role in the proof of Macdonald Conjectures [@Ch4] and are a natural generalization of affine Hecke algebras, which are an object of great importance in representation theory.

In the paper [@EG] Pavel Etingof and Victor Ginzburg studied the rational degeneration of a double affine Hecke algebra. They discovered that in the case 