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arXiv · 2509.06320

On the Casimir number and formal codegree of Haagerup-Izumi fusion rings

Ying Zheng·Jiacheng Bao·Zhiqiang Yu
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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.

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Ying Zheng, Jiacheng Bao, Zhiqiang Yu. 2025-09-08. On the Casimir number and formal codegree of Haagerup-Izumi fusion rings. https://arxiv.org/abs/2509.06320

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