Graphical calculus for quantum vertex operators, I: The dynamical fusion operator
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910717127426048 |
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| author | De Clercq, Hadewijch Reshetikhin, Nicolai Stokman, Jasper |
| author_facet | De Clercq, Hadewijch Reshetikhin, Nicolai Stokman, Jasper |
| contents | This paper is the first in a series on graphical calculus for quantum vertex operators. We establish in great detail the foundations of graphical calculus for ribbon categories and braided monoidal categories with twist. We illustrate the potential of this approach by applying it to various categories of quantum group modules, in particular to derive an extension of the linear operator equation for dynamical fusion operators, due to Arnaudon, Buffenoir, Ragoucy and Roche, to a system of linear operator equations of $q$-KZ type. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_09464 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Graphical calculus for quantum vertex operators, I: The dynamical fusion operator De Clercq, Hadewijch Reshetikhin, Nicolai Stokman, Jasper Quantum Algebra Mathematical Physics 17B37, 17B69, 18M15, 81R50 This paper is the first in a series on graphical calculus for quantum vertex operators. We establish in great detail the foundations of graphical calculus for ribbon categories and braided monoidal categories with twist. We illustrate the potential of this approach by applying it to various categories of quantum group modules, in particular to derive an extension of the linear operator equation for dynamical fusion operators, due to Arnaudon, Buffenoir, Ragoucy and Roche, to a system of linear operator equations of $q$-KZ type. |
| title | Graphical calculus for quantum vertex operators, I: The dynamical fusion operator |
| topic | Quantum Algebra Mathematical Physics 17B37, 17B69, 18M15, 81R50 |
| url | https://arxiv.org/abs/2205.09464 |