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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Double affine Hecke algebras and Calogero-Moser spaces
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by Alexei Oblomkov
Represent. Theory 8 (2004), 243-266
Published electronically: June 2, 2004


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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Bibliographic 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