Representations of Cyclotomic Rational Cherednik Algebras with   Aspherical Parameters

Huijun Zhao

arXiv:1809.06724·math.RT·September 19, 2018

Representations of Cyclotomic Rational Cherednik Algebras with Aspherical Parameters

Huijun Zhao

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Abstract

In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_{c}$ and its spherical subalgebra $e H_{c} e$ with a Weil generic aspherical parameter $c$ , and further describe the simple modules in the category $O_{c}^{s p h}$ . The main tools we use are categorical Kac-Moody actions on catogories $O_{c}$ and restriction functors for Harish-Chandra bimodules.

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TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra