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arXiv · 2504.14042

Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs

Jian-Rong Li·Tomasz Przezdziecki
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Abstract

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.

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BibTeXRIS

Jian-Rong Li, Tomasz Przezdziecki. 2025-04-18. Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs. https://arxiv.org/abs/2504.14042

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