Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917431835885568 |
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| author | Li, Jian-Rong Przezdziecki, Tomasz |
| author_facet | Li, Jian-Rong Przezdziecki, Tomasz |
| contents | We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type $\mathsf{AI}$. By computing the action of the generators in Lu and Wang's Drinfeld-type presentation on Gelfand-Tsetlin bases, we determine the spectrum of a large commutative subalgebra arising from the Lu-Wang presentation. This leads to an explicit formula for boundary analogues of $q$-characters in the setting of quantum affine symmetric pairs. We interpret this formula combinatorially in terms of semistandard Young tableaux. Our results imply that boundary $q$-characters share familiar features with ordinary $q$-characters - such as a version of the highest weight property - yet they also display new phenomena, including an extra symmetry. In particular, we provide the first examples of boundary $q$-characters for quantum affine symmetric pairs that do not arise from restriction of ordinary $q$-characters, thereby revealing genuinely new structures in this new setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs Li, Jian-Rong Przezdziecki, Tomasz Representation Theory Quantum Algebra We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type $\mathsf{AI}$. By computing the action of the generators in Lu and Wang's Drinfeld-type presentation on Gelfand-Tsetlin bases, we determine the spectrum of a large commutative subalgebra arising from the Lu-Wang presentation. This leads to an explicit formula for boundary analogues of $q$-characters in the setting of quantum affine symmetric pairs. We interpret this formula combinatorially in terms of semistandard Young tableaux. Our results imply that boundary $q$-characters share familiar features with ordinary $q$-characters - such as a version of the highest weight property - yet they also display new phenomena, including an extra symmetry. In particular, we provide the first examples of boundary $q$-characters for quantum affine symmetric pairs that do not arise from restriction of ordinary $q$-characters, thereby revealing genuinely new structures in this new setting. |
| title | Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2504.14042 |