Twists of rational Cherednik algebras
Quantum Algebra
2025-01-14 v2 Representation Theory
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 , when 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.
Keywords
Cite
@article{arxiv.2205.11971,
title = {Twists of rational Cherednik algebras},
author = {Yuri Bazlov and Arkady Berenstein and Edward Jones-Healey and Alexander McGaw},
journal= {arXiv preprint arXiv:2205.11971},
year = {2025}
}
Comments
18 pages; v2: fixed a typo (epsilon -> 1/epsilon in reflection formula), results unchanged