Work

A Serre-type presentation for $\imath$quantum supergroups of type A

Year: 2026

Type: preprint

Abstract: We establish a Serre-type presentation for $\imath$quantum 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.02176

Authors: Cui, Weideng, Shen, Yaolong

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Science and Technology Commission of Shanghai Municipality

Award: G1609915050

OpenAlex ID: W7207778758

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