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

2025/04/18 by Li, Jian-Rong, Przezdziecki, Tomasz · 2 citations
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.14042

Abstract

We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type 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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• Braid group action and quasi-split affine iquantum groups III
• GKLO representations of twisted Yangians in type AI and quantizations of symmetric quotients of the affine Grassmannian

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