Burnside type results for fusion rings

S Burciu, S Palcoux - arXiv preprint arXiv:2302.07604, 2023 - arxiv.org
In this paper, we extend a classical vanishing result of Burnside from the character tables of
finite groups to the character tables of commutative fusion rings, or more generally to a …

Interpolated family of non-group-like simple integral fusion rings of Lie type

Z Liu, S Palcoux, Y Ren - International Journal of Mathematics, 2023 - World Scientific
This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal
subfactor. We compute the generic fusion rules of the Grothendieck ring of Rep (PSL (2, q)) …

On a necessary condition for unitary categorification of fusion rings

P Etingof, D Nikshych, V Ostrik - arXiv preprint arXiv:2102.13239, 2021 - arxiv.org
In arXiv: 1910.12059 Liu, Palcoux and Wu proved a remarkable necessary condition for a
fusion ring to admit a unitary categorification, by constructing invariants of the fusion ring that …