Extended Baxter relations and QQ-systems for quantum affine algebras
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909369641205760 |
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| author | Frenkel, Edward Hernandez, David |
| author_facet | Frenkel, Edward Hernandez, David |
| contents | Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in the category O of representations of the Borel subalgebra of the quantum affine algebra U_q(g^), which we established in our earlier works arXiv:1308.3444 and arXiv:1606.05301. In the present paper, we conjecture a family of analogous relations labeled by elements of the Weyl group W of g, so that the original relations correspond to the identity element. These relations are closely connected to the W-symmetry of q-characters established in arXiv:2211.09779. We prove these relations for all w in W if g has rank two, and we prove the extended TQ-relations if w is a simple reflection. We also generalize our results and conjectures to the shifted quantum affine algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_13256 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extended Baxter relations and QQ-systems for quantum affine algebras Frenkel, Edward Hernandez, David Quantum Algebra Statistical Mechanics High Energy Physics - Theory Representation Theory Exactly Solvable and Integrable Systems Generalized Baxter's TQ-relations and the QQ-system are systems of algebraic relations in the category O of representations of the Borel subalgebra of the quantum affine algebra U_q(g^), which we established in our earlier works arXiv:1308.3444 and arXiv:1606.05301. In the present paper, we conjecture a family of analogous relations labeled by elements of the Weyl group W of g, so that the original relations correspond to the identity element. These relations are closely connected to the W-symmetry of q-characters established in arXiv:2211.09779. We prove these relations for all w in W if g has rank two, and we prove the extended TQ-relations if w is a simple reflection. We also generalize our results and conjectures to the shifted quantum affine algebras. |
| title | Extended Baxter relations and QQ-systems for quantum affine algebras |
| topic | Quantum Algebra Statistical Mechanics High Energy Physics - Theory Representation Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2312.13256 |