与 q-analog Virasoro-like Lie algebra 有关的 [公式省略] 系列的表示

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-06 DOI:10.1016/j.laa.2024.06.028

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引用次数: 0

摘要

本文研究了与 q-analog Virasoro-like Lie algebra 相关的无穷维李代数的表示。我们给出了最高权重的不可还原模块是哈里什-钱德拉模块的必要条件和充分条件。我们证明了 Verma 模块要么是不可还原的，要么有相应的不可还原最高权重模块是 Harish-Chandra 模块。我们还给出了 Verma 模块的最大适当子模块，以及当最高权重满足某些自然条件时，不可还原最高权重模块的-特征。此外，我们还给出了具有非难中心电荷的哈里什-钱德拉模块的分类。

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Representations of the C-series related to the q-analog Virasoro-like Lie algebra

In this paper, we study the representation of an infinite-dimensional Lie algebra $C$ related to the q-analog Virasoro-like Lie algebra. We give the necessary and sufficient conditions for the highest weight irreducible module $V (ϕ)$ of $C$ to be a Harish-Chandra module. We prove that the Verma $C$ -module $\bar{V} (ϕ)$ is either irreducible or has the corresponding irreducible highest weight $C$ -module $V (ϕ)$ that is a Harish-Chandra module. We also give the maximal proper submodule of the Verma module $\bar{V} (ϕ)$ and the e-character of the irreducible highest weight $C$ -module $V (ϕ)$ when the highest weight ϕ satisfies some natural conditions. Furthermore, we give the classification of the Harish-Chandra $C$ -modules with nontrivial central charge.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.