when this algebra has a nontrivial center, the spectrum of the center is isomorphic to the so called Calogero-Moser space, and this isomorphism respects the Poisson structure. The Calogero-Moser space first appeared in [@KKS] as a completed configuration space for the Calogero-Moser integrable system. Recently attention to this object was aroused by the paper [@W].

The isomorphism between the spectrum of the center of the degenerate double affine Hecke algebra and the Calogero-Moser space gives an interpretation of the degenerate double affine Hecke algebra as an Azumaya algebra in the case when the Calogero-Moser space is smooth.

In the present paper we study the double affine Hecke algebra $H$ with $q=1$. In this case the algebra has a nontrivial center. We establish a Poisson isomorphism between the spectrum of the center $Z(H)$ of $H$ and a relativistic analog of the Calogero-Moser space in the case of the root system $A_{n-1}$. The relativistic analog of the Calogero-Moser space is a completed configuration space for the so called Ruijsenaars-Shneider (or briefly RS) integrable system [@RS].

For the general algebra $H$ (with $q=1$) we prove that the ring $Z(H)$ has no zero divisors, and that it is a normal, Cohen-Macaulay ring isomorphic to 