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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.11061 |
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| _version_ | 1866914951935819776 |
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| author | Nomura, Kazumasa Terwilliger, Paul |
| author_facet | Nomura, Kazumasa Terwilliger, Paul |
| contents | Let $Γ$ denote a distance-regular graph, with vertex set $X$ and diameter $D\geq 3$. We assume that $Γ$ is formally self-dual and $q$-Racah type. We also assume that for each $x \in X$ the subconstituent algebra $T=T(x)$ contains a certain central element $Z=Z(x)$. We use $Z$ to construct a spin model $\sf W$ afforded by $Γ$. We investigate the combinatorial implications of $Z$. We reverse the logical direction and recover $Z$ from $\sf W$. We finish with some open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11061 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spin models and distance-regular graphs of $q$-Racah type Nomura, Kazumasa Terwilliger, Paul Combinatorics Quantum Algebra 05E30 Let $Γ$ denote a distance-regular graph, with vertex set $X$ and diameter $D\geq 3$. We assume that $Γ$ is formally self-dual and $q$-Racah type. We also assume that for each $x \in X$ the subconstituent algebra $T=T(x)$ contains a certain central element $Z=Z(x)$. We use $Z$ to construct a spin model $\sf W$ afforded by $Γ$. We investigate the combinatorial implications of $Z$. We reverse the logical direction and recover $Z$ from $\sf W$. We finish with some open problems. |
| title | Spin models and distance-regular graphs of $q$-Racah type |
| topic | Combinatorics Quantum Algebra 05E30 |
| url | https://arxiv.org/abs/2308.11061 |