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arXiv · 2205.11971

Twists of rational Cherednik algebras

Yuri Bazlov·Arkady Berenstein·Edward Jones-Healey·Alexander McGaw
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Abstract

We show that braided Cherednik algebras introduced by the first two authors 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.

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Yuri Bazlov, Arkady Berenstein, Edward Jones-Healey, Alexander McGaw. 2022-05-24. Twists of rational Cherednik algebras. https://doi.org/10.1093/qmath%2Fhaac033

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