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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.17109 |
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| _version_ | 1866909214181425152 |
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| author | Sugawara, Masaru |
| author_facet | Sugawara, Masaru |
| contents | In arXiv:0912.1346, four quantum dilogarithm identities containing infinitely many factors are proposed as wall-crossing formula for refined BPS invariant. We give algebraic proof of these identities using the formula for universal R-matrix of quantum affine algebra developed by K. Ito, which yields various product presentation of universal R-matrix by choosing various convex orders on affine root system. By the uniqueness of universal R-matrix and appropriate degeneration, we can construct various quantum dilogarithm identities including the ones proposed in arXiv:0912.1346, which turn out to correspond to convex orders of multiple row type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17109 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum dilogarithm identities arising from the product formula for universal R-matrix of quantum affine algebras Sugawara, Masaru Quantum Algebra 17B37 (Primary), 17B81 (Secondary) In arXiv:0912.1346, four quantum dilogarithm identities containing infinitely many factors are proposed as wall-crossing formula for refined BPS invariant. We give algebraic proof of these identities using the formula for universal R-matrix of quantum affine algebra developed by K. Ito, which yields various product presentation of universal R-matrix by choosing various convex orders on affine root system. By the uniqueness of universal R-matrix and appropriate degeneration, we can construct various quantum dilogarithm identities including the ones proposed in arXiv:0912.1346, which turn out to correspond to convex orders of multiple row type. |
| title | Quantum dilogarithm identities arising from the product formula for universal R-matrix of quantum affine algebras |
| topic | Quantum Algebra 17B37 (Primary), 17B81 (Secondary) |
| url | https://arxiv.org/abs/2210.17109 |