论文标题
结构常数，以撒属性和扩展的Haagerup融合类别
Structure constants, Isaacs property and Extended Haagerup fusion categories
论文作者
论文摘要
本文提出了一个抽象的ISAACS属性，该属性涉及融合环的傅立叶变换，这可能是非交通的，因此扩展了[12]中描述的交换版本。随后在[8]中针对任何球形融合类别中引入了该属性的一个分类版本，与我们的伪独立案例中的抽象版本相匹配。我们证明，在交换案例中，ISAACS的财产占据了独特的位置，属于结构常数和1-Frobenius属性之间。我们表明，被称为EHI的扩展Haagerup融合类别不满足以撒的财产。这一发现提供了对[8，问题5.8]，反驳[12，猜想2.5]的负面反应，并恢复了EH1缺乏编织结构。
This paper presents an abstract Isaacs property that involves the Fourier transform for fusion rings, which may be non-commutative, thus expanding upon the commutative version described in [12]. A categorical version of this property was subsequently introduced in [8] for any spherical fusion category, matching with our abstract version in the pseudo-unitary case. We demonstrate that the Isaacs property occupies a distinct position, falling between the integrality of structure constants and the 1-Frobenius properties, in the commutative case. We show that the Extended Haagerup fusion categories, denoted as EHi, do not satisfy the Isaacs property. This finding provides a negative response to [8, Question 5.8], refutes [12, Conjecture 2.5], and recovers that EH1 lacks a braiding structure.
