Zhanqiang Bai

activity

20232026

collaborators

10 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 $L (λ)$ be a simple highest weight module of a classical Lie algebra $g$ with highest weight $λ - ρ$ , where $ρ$ is half the sum of positive roots. Joseph proved that th…

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 $L (λ)$ be a highest weight module of $g$ with highest weight $λ - ρ$ , where $ρ$ is half the sum of positive roots. A…

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 $L (λ)$ a highest weight Harish-Chandra module of $G_{R}$ with highest weight $λ$ . In this article, we exhibit a…

math.RT2025

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

Zhanqiang Bai, Fan Gao, Yutong Wang +1

Let $L (λ)$ be an irreducible highest weight module of a complex simple Lie algebra of exceptional type, with highest weight $λ - ρ$ , where $ρ$ is half the sum of positive roots. Its…

math.RT2024

A characterization of unitarity of some highest weight Harish-Chandra modules

Zhanqiang Bai, Markus Hunziker

Let $L (λ)$ be a highest weight Harish-Chandra module with highest weight $λ$ . When the associated variety of $L (λ)$ is not maximal, that is, not equal to the nilradical of the corr…

math.RT2024

On the associated variety of a highest weight Harish-Chandra module

Zhanqiang Bai, Markus Hunziker, Xun Xie +1

We prove a simple formula that calculates the associated variety of a highest weight Harish-Chandra module directly from its highest weight. We also give a formula for the Gelfand-…

math.RT2023

Irreducible representations of $GL_{n} (C)$ of minimal Gelfand-Kirillov dimension

Zhanqiang Bai, Yangyang Chen, Dongwen Liu +1

In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of $G = GL_{n} (C)$ p…

math.RT2023

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…

math.RT2023

An explicit characterization of socular simple modules of $sl (n, C)$

Zhanqiang Bai, Wei Xiao, Xun Xie

Let $g$ be a simple complex Lie algebra with a Cartan subalgebra $h$ . We fix a standard parabolic subalgebra $p \supset h$ . The socular s…

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

Symmetry Regularization of 1D Generalized Coulomb Problems

Associated varieties of integral minimal highest weight modules

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

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

A characterization of unitarity of some highest weight Harish-Chandra modules

On the associated variety of a highest weight Harish-Chandra module

Irreducible representations of GLn​(C) of minimal Gelfand-Kirillov dimension

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

An explicit characterization of socular simple modules of sl(n,C)

Irreducible representations of $GL_{n} (C)$ of minimal Gelfand-Kirillov dimension

An explicit characterization of socular simple modules of $sl (n, C)$