arXiv subjects

Hongying Zhu

Publications and source records attributed to Hongying Zhu.

2 recordsLinked to original sources

arXiv2025

Quantum queer superalgebra and its integral form

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.

math.QA↗

arXiv2024

Braid Group Action and Quantum Queer Superalgebra

In this paper, we present explicit actions of braid group on the universal enveloping superalgebra ${\boldsymbol U}(\mathfrak{q}_n)$ and the quantum queer superalgebra ${\boldsymbol U}_{\!{v}}(\mathfrak{q}_{n})$. Then we provide a new definition of root vectors and some explicit expression for them. With these procedures, we obtain the PBW-type basis containing the product of root vectors.

math.QA↗