Double affine Hecke algebras and Calogero-Moser spaces
Oblomkov, A.
arXiv, 0303190 / Harvested from arXiv
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 $H_{1,\tau}=End_{eH_{1,\tau}e}(H_{1,\tau}e)$. 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 $eH_{1,\tau}$ is projective and all irreducible finite dimensional representations of $H_{1,\tau}$ are regular representation of the finite Hecke algebra.
Publié le : 2003-03-15
Classification:  Mathematics - Representation Theory,  Mathematical Physics
@article{0303190,
     author = {Oblomkov, A.},
     title = {Double affine Hecke algebras and Calogero-Moser spaces},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303190}
}
Oblomkov, A. Double affine Hecke algebras and Calogero-Moser spaces. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303190/