Genqiang Liu

activity

20222026

collaborators

6 papers

math.RT2026

Classification of Simple Cuspidal Modules over Nongraded Witt Lie Algebras

Genqiang Liu, Xiaoyao Zheng, Yufang Zhao

For a positive integer $n$ , let $A_{n} = C [t_{1}^{\pm 1}, \dots, t_{n}^{\pm 1}, x_{1}, \dots, x_{n}]$ and $g_{n} = ⨁_{i = 1}^{n} A_{n} d_{i}$ , where $d_i=t_i\frac{\partial}{\partial…

math.RT2026

The category of Whittaker modules over the Cartan Type Lie algebra $S ˉ_{2}$

Xiaoyao Zheng, Yufang Zhao, Genqiang Liu

The Lie algebra $S ˉ_{2}$ of polynomial vector fields on $C^{2}$ with constant divergence is an important Cartan type Lie algebra. In this paper, we study Whittaker $\bar{…

math.RT2025

Irreducible cuspidal $sl_{n + 1}$ -modules from finite-dimensional modules over the minimal nilpotent finite $W$ -algebra

Genqiang Liu, Mingjie Li

A weight $sl_{n + 1}$ -module with finite-dimensional weight spaces is called a cuspidal module, if every root vector of $sl_{n + 1}$ acts injectively on it. In \c…

math.RT2024

Minimal nilpotent finite $W$ -algebra and cuspidal module category of $sp_{2 n}$

Genqiang Liu, Mingjie Li

Let $U_{S}$ be the localization of $U (sp_{2 n})$ with respect to the Ore subset $S$ generated by the root vectors $X_{ε_{1} - ε_{2}}, \dots, X_{ε_{1} - ε_{n}}, X_{2 ε_{1}}$ . We show that th…

math.RT2023

A category equivalence on the Lie algebra of polynomial vector fields

Genqiang Liu, Yufang Zhao

For any positive integer $n$ , let $W_{n} = Der (C [t_{1}, \dots, t_{n}])$ . The subspaces $\mathfrak{h}_n=\text{Span}\{t_1\frac{\partial}{\partial{t_1}},\dots,t_n\frac{\partial}…

math.RT2022

Category $O$ for the Lie algebra of vector fields on the line

Genqiang Liu, Mingjie Li

Let $W$ be the Lie algebra of vector fields on the line. Via computing extensions between all simple modules in the category $O$ , we give the block decompositi…

Classification of Simple Cuspidal Modules over Nongraded Witt Lie Algebras

The category of Whittaker modules over the Cartan Type Lie algebra Sˉ2​

Irreducible cuspidal sln+1​-modules from finite-dimensional modules over the minimal nilpotent finite W-algebra

Minimal nilpotent finite W-algebra and cuspidal module category of sp2n​

A category equivalence on the Lie algebra of polynomial vector fields

Category O for the Lie algebra of vector fields on the line

The category of Whittaker modules over the Cartan Type Lie algebra $S ˉ_{2}$

Irreducible cuspidal $sl_{n + 1}$ -modules from finite-dimensional modules over the minimal nilpotent finite $W$ -algebra

Minimal nilpotent finite $W$ -algebra and cuspidal module category of $sp_{2 n}$

Category $O$ for the Lie algebra of vector fields on the line