有理Cherednik代数的扭曲

IF 0.6 4区数学 Q3 MATHEMATICS

Quarterly Journal of Mathematics Pub Date : 2022-11-14 DOI:10.1093/qmath/haac033

Y Bazlov, E Jones-Healey, A Mcgaw, A Berenstein

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引用次数: 0

摘要

证明了当m为偶数时，Bazlov和Berenstein引入的辫状Cherednik代数是非原复反射群G(m,p,n)$的有理Cherednik代数的环扭转。给出了具有量子多项式不变量Artin-Schelter正则环的神秘反射群的一种新构造。作为这个结果的一个应用，我们证明了一个编织Cherednik代数有有限维表示当且仅当它的有理对应物有有限维表示。

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Twists of rational Cherednik algebras

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.

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来源期刊

Quarterly Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.