Zhanqiang Bai

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20232026

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8 papers · 1 filter

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.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

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

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-…