On Interpolation Categories for the Hyperoctahedral Group

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-04-01 DOI:10.1007/s10468-025-10331-y

Th. Heidersdorf, G. Tyriard

引用次数: 0

Abstract

Two different types of Deligne categories have been defined to interpolate the finite dimensional complex representations of the hyperoctahedral group. The first one, initially defined by Knop and then further studied by Likeng and Savage, uses a categorical analogue of the permutation representation as a tensor generator. The second one, due to Flake and Maassen, is tensor generated by a categorical analogue of the reflection representation. We construct a symmetric monoidal functor between the two and show that it is an equivalence of symmetric monoidal categories.

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关于高八面体群的插值范畴

定义了两种不同类型的Deligne范畴来插值高八面体群的有限维复表示。第一种方法最初由Knop定义，然后由Likeng和Savage进一步研究，它使用排列表示的分类模拟作为张量生成器。第二个，由于Flake和Maassen，是由反射表示的分类模拟生成的张量。在这两者之间构造了一个对称一元函子，并证明了它是对称一元范畴的等价。

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

Algebras and Representation Theory 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： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.