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arXiv · 2210.13936

Structure constants, Isaacs property and Extended Haagerup fusion categories

Sebastian Burciu·Sebastien Palcoux
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Abstract

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.

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BibTeXRIS

Sebastian Burciu, Sebastien Palcoux. 2022-10-25. Structure constants, Isaacs property and Extended Haagerup fusion categories. https://doi.org/10.1080/00927872.2024.2412181

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