Microlocal $KZ$-functors and rational Cherednik algebras
Kevin McGerty
Source: Duke Math. J. Volume 161, Number 9
(2012), 1657-1709.
Abstract
Following the work of Kashiwara and Rouquier and of Gan and Ginzburg, we define a family of exact functors from category $\mathcal{O}$ for the rational Cherednik algebra in type $A$ to representations of certain colored braid groups and we calculate the dimensions of the representations thus obtained from standard modules. To show that our constructions make sense in a more general context, we also briefly study the case of the rational Cherednik algebra corresponding to complex reflection group $\mathbb{Z}/l\mathbb{Z}$.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1338987166
Digital Object Identifier: doi:10.1215/00127094-1593353
Zentralblatt MATH identifier: 06053747
Mathematical Reviews number (MathSciNet): MR2942791
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