Structure constants, Isaacs property and extended Haagerup fusion categories.

AbstractThis paper extends the Isaacs property, originally introduced by the second author, to noncommutative fusion rings through the use of a Fourier transform. It aligns this property with a subsequent categorical equivalent for spherical fusion categories described by Etingof et al., particularly in the pseudounitary case. Within the commutative framework, the Isaacs property is situated strictly between the integrality of structure constants and the 1- Frobenius properties. Furthermore, the paper demonstrates that the Extended Haagerup fusion categories (denoted as EHi) do not possess the Isaacs property, thus providing a negative answer to questions posed by the aforementioned researchers. It also reaffirms that EH1 lacks a braiding structure. [ABSTRACT FROM AUTHOR]