## Double affine Hecke algebras and Calogero-Moser spaces

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- by Alexei Oblomkov
- Represent. Theory
**8**(2004), 243-266 - DOI: https://doi.org/10.1090/S1088-4165-04-00246-8
- Published electronically: June 2, 2004
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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.## References

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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: https://doi.org/10.1090/S1088-4165-04-00246-8
- MathSciNet review: 2077482