Quantum queer superalgebra and its integral form

2025/09/29 by Chen, Jianmin, Li, Zhenhua, Zhu, Hongying
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2509.24265

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, Z}. This yields an explicit presentation of \boldsymbol U_{v, Z} and provides a way to understand the structure of the quantum queer superalgebra at roots of unity.

Citations

• Braid Group Action and Quantum Queer Superalgebra
• Some multiplication formulas in queer q-Schur superalgebras

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• Quantum queer supergroups via v-differential operators
• The first fundamental theorem of invariant theory for the quantum queer superalgebra
• Central elements and evaluation map for the quantum queer superalgebras
• Braided tensor products and polynomial invariants for the quantum queer superalgebra