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arXiv math/0303190math.RTmath-phmath.MP
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双仿射Hecke代数与Calogero-Moser空间

Double affine Hecke algebras and Calogero-Moser spaces

A. Oblomkov

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摘要：

本文证明了二重仿射Hecke代数$H_{1,τ}$的球面子代数$eH_{1,τ}e$是与$H_{1,τ}$的中心$Z$同构的积分Cohen-Macaulay代数，并且$H_{1,τ}e$是具有性质$H_{1,τ}=End_{eH_{1,τ}e}(H_{1,τ}e)$的Cohen-Macaulay $eH_{1,τ}e$ -模.在根系$A_{n-1}$的情况下，品种$Spec(Z)$是光滑的，并符合三角Calogero-Moser系统的相对论模拟的位形空间的完成。这意味着Cherednik的结果，即模$eH_{1,τ}$是投射的，并且$H_{1,τ}$的所有不可约有限维表示是有限Hecke代数的正则表示.

英文摘要：

In 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.

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