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Representation Theory

ISSN 1088-4165



Double affine Hecke algebras and Calogero-Moser spaces

Author: Alexei Oblomkov
Journal: Represent. Theory 8 (2004), 243-266
MSC (2000): Primary 13C14, 15A27, 16H05
Published electronically: June 2, 2004
MathSciNet review: 2077482
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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 $H_{1,\tau }=\operatorname {End}_{eH_{1,\tau }e}(H_{1,\tau }e)$ when $\tau$ is not a root of unity. In the case of the root system $A_{n-1}$ the variety $\operatorname {Spec}(Z)$ is smooth and coincides with the completion of the configuration space of the Ruijenaars-Schneider system. It implies that the module $eH_{1,\tau }$ is projective and all irreducible finite dimensional representations of $H_{1,\tau }$ are isomorphic to the regular representation of the finite Hecke algebra.

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Additional Information

Alexei Oblomkov
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139

Received by editor(s): July 10, 2003
Received by editor(s) in revised form: April 26, 2004
Published electronically: June 2, 2004
Additional Notes: This work was partially supported by the NSF grant DMS-9988796
Article copyright: © Copyright 2004 American Mathematical Society