Strong duality Data of type $A$ and extended $T$-systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917675275386880 |
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| author | Naoi, Katsuyuki |
| author_facet | Naoi, Katsuyuki |
| contents | The extended $T$-systems are a number of short exact sequences in the category of finite-dimensional modules over the quantum affine algebras of types $A_n^{(1)}$ and $B_n^{(1)}$, introduced by Mukhin and Young as a generalization of the $T$-systems. In this paper we establish the extended $T$-systems for more general modules, which are constructed from an arbitrary strong duality datum of type $A$. Our approach does not use the theory of $q$-characters, and so also provides a new proof to the original Mukhin-Young's extended $T$-systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15681 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong duality Data of type $A$ and extended $T$-systems Naoi, Katsuyuki Quantum Algebra Representation Theory 17B37, 81R50, 17B10 The extended $T$-systems are a number of short exact sequences in the category of finite-dimensional modules over the quantum affine algebras of types $A_n^{(1)}$ and $B_n^{(1)}$, introduced by Mukhin and Young as a generalization of the $T$-systems. In this paper we establish the extended $T$-systems for more general modules, which are constructed from an arbitrary strong duality datum of type $A$. Our approach does not use the theory of $q$-characters, and so also provides a new proof to the original Mukhin-Young's extended $T$-systems. |
| title | Strong duality Data of type $A$ and extended $T$-systems |
| topic | Quantum Algebra Representation Theory 17B37, 81R50, 17B10 |
| url | https://arxiv.org/abs/2305.15681 |