PreprintCC BY-NC-ND 4.0arXiv
Shifted quantum affine symmetric pairs: finite presentations and graded coideal structures
Abstract
Shifted quantum affine symmetric pair algebras were recently introduced as a trigonometric analogue of shifted twisted Yangians, whose truncations are expected to quantize fixed point loci in generalized affine Grassmannian slices. They are defined via a loop presentation with infinitely many generators and relations. In this paper, we consider anti-dominantly shifted quantum affine symmetric pair algebras of simply-laced split type. Our main result is a construction of a finite presentation à la Levendorskii. We apply it in type A to construct an embedding of a shifted quantum symmetric pair algebra into the corresponding shifted quantum affine algebra, yielding a graded coideal structure.
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BibTeX
@misc{li2026shifted,
title = {{Shifted quantum affine symmetric pairs: finite presentations and graded coideal structures}},
author = {Jian-Rong Li and Tomasz Przezdziecki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25597},
eprint = {2610.25597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25597},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Shifted quantum affine symmetric pairs: finite presentations and graded coideal structures
AU - Jian-Rong Li
AU - Tomasz Przezdziecki
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25597
UR - https://arxiv.org/abs/2610.25597
AB - Shifted quantum affine symmetric pair algebras were recently introduced as a trigonometric analogue of shifted twisted Yangians, whose truncations are expected to quantize fixed point loci in generalized affine Grassmannian slices. They are defined via a loop presentation with infinitely many generators and relations. In this paper, we consider anti-dominantly shifted quantum affine symmetric pair algebras of simply-laced split type. Our main result is a construction of a finite presentation à la Levendorskii. We apply it in type A to construct an embedding of a shifted quantum symmetric pair algebra into the corresponding shifted quantum affine algebra, yielding a graded coideal structure.
ER -