PreprintCC0arXiv
A Serre-type presentation for imathquantum supergroups of type A
Abstract
We establish a Serre-type presentation for imathquantum enveloping superalgebras arising from quantum supersymmetric pairs of type A. We first prove, in arbitrary type, that evaluating a quantum Serre polynomial on the coideal generators produces a correction of strictly smaller weight in the natural filtration using the projection technique. We then compute these remainder terms for all type A super Satake diagrams. In particular, we determine the new degree-four relations associated with isotropic odd simple roots of the relevant local Satake diagrams.
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BibTeX
@misc{cui2026serretype,
title = {{A Serre-type presentation for $\imath$quantum supergroups of type A}},
author = {Weideng Cui and Yaolong Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02176},
eprint = {2609.02176},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02176},
note = {CC0},
}
RIS
TY - UNPB
TI - A Serre-type presentation for imathquantum supergroups of type A
AU - Weideng Cui
AU - Yaolong Shen
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02176
UR - https://arxiv.org/abs/2609.02176
AB - We establish a Serre-type presentation for imathquantum enveloping superalgebras arising from quantum supersymmetric pairs of type A. We first prove, in arbitrary type, that evaluating a quantum Serre polynomial on the coideal generators produces a correction of strictly smaller weight in the natural filtration using the projection technique. We then compute these remainder terms for all type A super Satake diagrams. In particular, we determine the new degree-four relations associated with isotropic odd simple roots of the relevant local Satake diagrams.
ER -