NIM-representations of Tambara-Yamagami generalizations

TL;DR

This paper classifies and computes NIM-representations of two generalizations of Tambara-Yamagami fusion rings, linking them to algebra objects, advancing understanding of their algebraic structures.

Contribution

It provides a complete classification of NIM-representations for two Tambara-Yamagami generalizations and identifies associated algebra objects, a novel extension in the field.

Findings

Classified irreducible NIM-representations for both generalizations.

Connected NIM-representations to specific algebra objects.

Enhanced understanding of the algebraic structure of these fusion rings.

Abstract

We compute and classify the irreducible non-negative integer matrix (NIM-)representations of two proposed generalizations of the Tambara-Yamagami fusion ring, as studied by Jordan-Larson and Galindo-Lentner-M\"oller, respectively. We also detect the algebra objects associated to these NIM-representations.