Twists of rational Cherednik algebras

Yuri Bazlov; Edward Jones-Healey; Alexander Mcgaw; Arkady Berenstein

doi:10.1093/qmath/haac033

Twists of rational Cherednik algebras

Yuri Bazlov, Edward Jones-Healey, Alexander Mcgaw, Arkady Berenstein

University of Oregon

Research output: Contribution to journal › Article › peer-review

Abstract

We show that braided Cherednik algebras introduced by Bazlov and Berenstein are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when m is even. This gives a new construction of mystic reflection groups which have Artin–Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra has a finite-dimensional representation if and only if its rational counterpart has one.

Original language	English
Article number	haac03
Pages (from-to)	1-18
Number of pages	18
Journal	Quarterly Journal of Mathematics
Volume	2022
Early online date	11 Oct 2022
DOIs	https://doi.org/10.1093/qmath/haac033
Publication status	Published - 14 Nov 2022

Keywords

Quantum group
Reflection group
Cherednik algebra
Drinfeld twist

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10.1093/qmath/haac033Licence: CC BY

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AU - Jones-Healey, Edward

AU - Mcgaw, Alexander

AU - Berenstein, Arkady

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N2 - We show that braided Cherednik algebras introduced by Bazlov and Berenstein are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when m is even. This gives a new construction of mystic reflection groups which have Artin–Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra has a finite-dimensional representation if and only if its rational counterpart has one.

AB - We show that braided Cherednik algebras introduced by Bazlov and Berenstein are cocycle twists of rational Cherednik algebras of the imprimitive complex reflection groups $G(m,p,n)$, when m is even. This gives a new construction of mystic reflection groups which have Artin–Schelter regular rings of quantum polynomial invariants. As an application of this result, we show that a braided Cherednik algebra has a finite-dimensional representation if and only if its rational counterpart has one.

KW - Quantum group

KW - Reflection group

KW - Cherednik algebra

KW - Drinfeld twist

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JF - Quarterly Journal of Mathematics

M1 - haac03

ER -

Twists of rational Cherednik algebras

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Keywords

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