Double Affine Hecke Algebras and Calogero-moser Spaces
نویسنده
چکیده
In this paper we prove that the spherical subalgebra eH1,τ e of the double affine Hecke algebra H1,τ is an integral Cohen-Macaulay algebra isomorphic to the center Z of H1,τ , and H1,τ e is a Cohen-Macaulay eH1,τ emodule with the property H1,τ = EndeH1,τ e(H1,τ e) when τ is not a root of unity. 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 RuijenaarsSchneider system. It implies that the module eH1,τ is projective and all irreducible finite dimensional representations of H1,τ are isomorphic to the regular representation of the finite Hecke algebra.
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