Solutions of 3D Reflection Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915694873935872 |
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| author | Inoue, Rei Kuniba, Atsuo |
| author_facet | Inoue, Rei Kuniba, Atsuo |
| contents | We construct a new solution $(R,K)$ to the three-dimensional reflection equation, a boundary analogue of the tetrahedron equation. The $R$-operator is the one obtained by Sun, Terashima, Yagi, and the authors in 2024, involving four quantum dilogarithms with arguments in the $q$-Weyl algebra. The new $K$-operator similarly involves ten such quantum dilogarithms. Our approach is based on the quantum cluster algebra associated with the symmetric butterfly quiver on the wiring diagram of type C. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solutions of 3D Reflection Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver Inoue, Rei Kuniba, Atsuo Quantum Algebra Mathematical Physics Exactly Solvable and Integrable Systems We construct a new solution $(R,K)$ to the three-dimensional reflection equation, a boundary analogue of the tetrahedron equation. The $R$-operator is the one obtained by Sun, Terashima, Yagi, and the authors in 2024, involving four quantum dilogarithms with arguments in the $q$-Weyl algebra. The new $K$-operator similarly involves ten such quantum dilogarithms. Our approach is based on the quantum cluster algebra associated with the symmetric butterfly quiver on the wiring diagram of type C. |
| title | Solutions of 3D Reflection Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver |
| topic | Quantum Algebra Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.22004 |