Duke Mathematical Journal

Microlocal KZ-functors and rational Cherednik algebras

Kevin McGerty

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Abstract

Following the work of Kashiwara and Rouquier and of Gan and Ginzburg, we define a family of exact functors from category 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 Z/lZ.

Article information

Source
Duke Math. J., Volume 161, Number 9 (2012), 1657-1709.

Dates
First available in Project Euclid: 6 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1338987166

Digital Object Identifier
doi:10.1215/00127094-1593353

Mathematical Reviews number (MathSciNet)
MR2942791

Zentralblatt MATH identifier
1290.16025

Subjects
Primary: 16S38: Rings arising from non-commutative algebraic geometry [See also 14A22]
Secondary: 53D55: Deformation quantization, star products 14A22: Noncommutative algebraic geometry [See also 16S38]

Citation

McGerty, Kevin. Microlocal $KZ$ -functors and rational Cherednik algebras. Duke Math. J. 161 (2012), no. 9, 1657--1709. doi:10.1215/00127094-1593353. https://projecteuclid.org/euclid.dmj/1338987166


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