On the Casimir number and formal codegree of Haagerup-Izumi fusion rings
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908551510753280 |
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| author | Zheng, Ying Bao, Jiacheng Yu, Zhiqiang |
| author_facet | Zheng, Ying Bao, Jiacheng Yu, Zhiqiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Casimir number and formal codegree of Haagerup-Izumi fusion rings Zheng, Ying Bao, Jiacheng Yu, Zhiqiang Quantum Algebra 18M20 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. |
| title | On the Casimir number and formal codegree of Haagerup-Izumi fusion rings |
| topic | Quantum Algebra 18M20 |
| url | https://arxiv.org/abs/2509.06320 |