the spherical subalgebra $eHe$ (where $e$ is the symmetrizer in the finite Hecke algebra). We also prove the equality $H=End_{eHe}(He)$, which allows us, in the case of the root system $A_{n-1}$, to interpret $H$ as an Azumaya algebra.

The techniques of the paper work also in the degenerate case and furnish a simpler proof of the results of [@EG]. Furthermore, there exists an intermediate degeneration of the double affine Hecke algebra which lies between the double affine Hecke algebra and the rational degeneration of this algebra. We call this algebra the trigonometric degeneration of the double affine Hecke algebra. The corresponding degeneration of the Calogero-Moser space yields the configuration space for the trigonometric Calogero-Moser system (sometimes this space is called the trigonometric Calogero-Moser space). The results of the paper hold for this intermediate degeneration and are given in the last section.

[**Acknowledgments.**]{} I’d like to thank my adviser Pavel Etingof for posing the problem, multiple explanations and help with proving many statements from the paper. I am especially grateful for the proof of Theorem 2. I am very grateful to Ivan Cherednik who helped me with the proof of Lemma \[lcom\]. I am also grateful to Victor Ostrik for very 