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arXiv · 2509.24265

Quantum queer superalgebra and its integral form

Jianmin Chen·Zhenhua Li·Hongying Zhu
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Abstract

In this paper, we introduce quantum root vectors for the quantum queer superalgebra ${\boldsymbol U}_{\!{v}}({\mathfrak q_n})$ via a braid-group action, compute their complete commutation relations, and construct a PBW-type basis for the Lusztig integral form ${{\boldsymbol U}_{v,\mathcal{ Z}}}$. This yields an explicit presentation of ${{\boldsymbol U}_{v,\mathcal{ Z}}}$ and provides a way to understand the structure of the quantum queer superalgebra at roots of unity.

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Jianmin Chen, Zhenhua Li, Hongying Zhu. 2025-09-29. Quantum queer superalgebra and its integral form. https://arxiv.org/abs/2509.24265

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