On the Casimir number and formal codegree of Haagerup-Izumi fusion rings
Ying Zheng, Jiacheng Bao, Zhiqiang Yu
Published: 2025/9/8
Abstract
For any cyclic group $\mathbb{Z}_n$, we first determine the Casimir number and determinant of the Haagerup-Izumi fusion ring $\mathcal{HI}_{\mathbb{Z}_n}$, it turns out that they do not share the same set of prime factors. Then we show that all finite-dimensional irreducible representations of $\mathcal{HI}_{\mathbb{Z}_n}$ are defined over certain cyclotomic fields. As a direct result, we obtain the formal codegrees of $\mathcal{HI}_{\mathbb{Z}_n}$, which satisfy the pseudo-unitary inequality.