Double affine Hecke algebras and Calogero-Moser spaces

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dc.creatorOblomkov, A.
dc.date2003-03-16
dc.date.accessioned2026-07-07T04:56:05Z
dc.date.available2026-07-07T04:56:05Z
dc.descriptionIn this paper we prove that the spherical subalgebra $eH_{1,τ}e$ of the double affine Hecke algebra $H_{1,τ}$ is an integral Cohen-Macaulay algebra isomorphic to the center $Z$ of $H_{1,τ}$, and $H_{1,τ}e$ is a Cohen-Macaulay $eH_{1,τ}e$-module with the property $H_{1,τ}=End_{eH_{1,τ}e}(H_{1,τ}e)$. In the case of the root system $A_{n-1}$ the variety $Spec(Z)$ is smooth and coincides with the completion of the configuration space of the relativistic analog of the trigomonetric Calogero-Moser system. This implies the result of Cherednik that the module $eH_{1,τ}$ is projective and all irreducible finite dimensional representations of $H_{1,τ}$ are regular representation of the finite Hecke algebra.
dc.description26 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0303190
dc.identifierhttp://arxiv.org/abs/math/0303190
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66799
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.titleDouble affine Hecke algebras and Calogero-Moser spaces
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