Twists of rational Cherednik algebras
Yuri Bazlov, Arkady Berenstein, Edward Jones-Healey, Alexander, McGaw

TL;DR
This paper demonstrates that braided Cherednik algebras are cocycle twists of rational Cherednik algebras for certain complex reflection groups, providing new insights into their structure and representations.
Contribution
It establishes a connection between braided and rational Cherednik algebras via cocycle twists, offering a novel construction of mystic reflection groups.
Findings
Braided Cherednik algebras are cocycle twists of rational Cherednik algebras for even m.
A braided Cherednik algebra has a finite-dimensional representation iff its rational counterpart does.
New construction of mystic reflection groups with Artin-Schelter regular rings.
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics
