On Interpolation Categories for the Hyperoctahedral GroupOn Interpolation Categories for the Hyperoctahedral GroupT. Heidersdorf, G. Tyriard

被引：0

作者：

Th. Heidersdorf ^{[1
]}

G. Tyriard ^{[2
]}

机构：

[1] Newcastle University,School of Mathematics, Statistics and Physics

[2] Universität Bonn,Mathematisches Institut

来源：

Algebras and Representation Theory | 2025年 / 28卷 / 2期

关键词：

Hyperoctahedral group; Tensor category; Deligne category; Invariant theory; Semisimplification; 17B10; 18D10; 20F55;

D O I：

10.1007/s10468-025-10331-y

中图分类号：

学科分类号：

摘要：

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.

引用

页码：613 / 646

页数：33