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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Double affine Hecke algebras and Calogero-Moser spaces
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by Alexei Oblomkov PDF
Represent. Theory 8 (2004), 243-266 Request permission


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
  • © Copyright 2004 American Mathematical Society
  • Journal: Represent. Theory 8 (2004), 243-266
  • MSC (2000): Primary 13C14, 15A27, 16H05
  • DOI:
  • MathSciNet review: 2077482