Double affine Hecke algebras and Calogero-Moser spaces

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In this paper we prove that the spherical subalgebra eH₁,τe of the double affine Hecke algebra H₁,τ is an integral Cohen-Macaulay algebra isomorphic to the center Z of H₁,τ, and H₁,τe is a Cohen-Macaulay eH₁,τe-module with the property H₁,τ=EndeH₁,τe(H₁,τe). In the case of the root system Aₙ₋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 eH₁,τ is projective and all irreducible finite dimensional representations of H₁,τ are regular representation of the finite Hecke algebra.