Representation Theory of Rational Cherednik Algebras of Type $\mathbb Z/l \mathbb Z$ via Microlocal Analysis

Kuwabara, Toshiro

doi:10.4171/PRIMS/97

Publications of the Research Institute for Mathematical Sciences

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Volume 49, Issue 1, 2013, pp. 87–110

DOI: 10.4171/PRIMS/97

Published online: 2013-03-02

Representation Theory of Rational Cherednik Algebras of Type $\mathbb Z/l \mathbb Z$ via Microlocal Analysis

Toshiro Kuwabara^[1]

(1) Higher School of Economics, Moscow, Russian Federation

Based on the methods developed in [KR], we consider microlocalization of rational Cherednik algebras of type $\mathbb Z/l \mathbb Z$. Our goal is to construct irreducible modules and standard modules of these rational Cherednik algebras by using microlocalization. As a consequence, we obtain sheaves corresponding to holonomic systems with regular singularities.

Keywords: rational Cherednik algebras, deformed preprojective algebras, microlocal analysis, regular holonomic systems

Kuwabara Toshiro: Representation Theory of Rational Cherednik Algebras of Type $\mathbb Z/l \mathbb Z$ via Microlocal Analysis. Publ. Res. Inst. Math. Sci. 49 (2013), 87-110. doi: 10.4171/PRIMS/97