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Representation theory of the rational Cherednik algebras of type Z/lZ via microlocal analysis

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

preprint2010arXivOpen access
Toshiro Kuwabara
math.RTmath.QAmath.AG
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Toshiro Kuwabara

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