Deformations of unitary Howe dual pairs

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI:10.1016/j.jpaa.2025.107948

Dan Ciubotaru , Hendrik De Bie , Marcelo De Martino , Roy Oste

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引用次数: 0

Abstract

We study deformations of the Howe pairs

(U (n), u (1, 1))

and

(U (n), u (1, 1 | 1))

to the context of a rational Cherednik algebra

H_{1, c} (G, E)

associated with a real reflection group G acting on a real vector space E of even dimension. For each pair, we show that the Lie (super)algebra structure of one partner is preserved under the deformation, which leads to a joint decomposition of the standard module or its tensor product with a spinor space. For the case where E is two-dimensional and G is a dihedral group, we provide complete descriptions for the deformed pair and the relevant joint-decomposition.

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幺正Howe对偶的变形

本文研究了在有理Cherednik代数H1，c（G，E）下的Howe对(U（n)， U(1,1)）和(U（n)， U(1,1|)）的变形，该代数与作用于偶数维的实向量空间E上的实反射群G有关。对于每一对，我们证明了在变形下一个伙伴的李（超）代数结构保持不变，从而导致标准模或其张量积与旋量空间的联合分解。对于E为二维，G为二面体群的情况，给出了变形对及其联合分解的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.