Zhanqiang Bai

activity

20242026

collaborators

8 papers

math.RT2026

A new proof for the partition algorithm of the annihilator varieties of highest weight modules

Zhanqiang Bai, Jing Jiang, Yongzhi Luan

Let $L (I^»)$ be a simple highest weight module of a classical Lie algebra $g$ with highest weight $I^» - I ¨ $ , where $I ¨ $ is half the sum of positive roots. Joseph proved tha…

math-ph2026

Symmetry Regularization of 1D Generalized Coulomb Problems

Zhanqiang Bai, Junwei Ma, Guowu Meng

For the 1D generalized Coulomb problems--a family that includes the quantizations of the 1D generalized Kepler problems of Ma-Meng-Xiao \cite{MMX2025}--we construct two explicit un…

math.RT2026

Associated varieties of integral minimal highest weight modules

Zhanqiang Bai, Jing Jiang, Rui Wang

Let $g$ be a complex simple Lie algebra and $L (I^»)$ be a highest weight module of $g$ with highest weight $I^» - I ¨ $ , where $I ¨ $ is half the sum of positive root…

math.RT2025

Unitarity of highest weight Harish-Chandra modules and smoothness of Schubert varieties

Zhanqiang Bai, William Q. Erickson, Markus Hunziker +1

Let $G_{R}$ be a Lie group of Hermitian type, and $L (I^»)$ a highest weight Harish-Chandra module of $G_{R}$ with highest weight $I^»$ . In this article, we exhibit…

math.RT2025

Gelfand-Kirillov dimensions and annihilator varieties of highest weight modules of exceptional Lie algebras

Zhanqiang Bai, Fan Gao, Yutong Wang +1

In this paper, we give an efficient algorithm to compute the Gelfand-Kirillov dimensions of simple highest weight modules of exceptional Lie algebras. By using the Sommers-Achar du…

math.RT2024

On the reducibility of scalar generalized Verma modules associated to two-step nilpotent parabolic subalgebras

Zhanqiang Bai, Minyan Fang, Zhaojun Wang

Let $g$ be a simple complex Lie algebra.A generalized Verma module induced from a one-dimensional representation of a parabolic subalgebra of $g$ is called a…