Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs
Abstract
We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type . 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 -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 -characters share familiar features with ordinary -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 -characters for quantum affine symmetric pairs that do not arise from restriction of ordinary -characters, thereby revealing genuinely new structures in this new setting.
Keywords
Cite
@article{arxiv.2504.14042,
title = {Boundary $q$-characters of evaluation modules for split quantum affine symmetric pairs},
author = {Jian-Rong Li and Tomasz Przezdziecki},
journal= {arXiv preprint arXiv:2504.14042},
year = {2026}
}