Gelfand-Kirillov dimensions and Reducibility of scalar type generalized Verma modules for classical Lie algebras

2022/05/11 by Zhanqiang Bai, Jing Jiang, Bai, Zhanqiang +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2205.05362

openalex publication_date 2022/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrakg be a classial Lie algebra and \mathfrakp be a maximal parabolic subalgebra. Let M be a generalized Verma module induced from a one dimensional representation of \mathfrakp. Such M is called a scalar type generalized Verma module. Its simple quotient L is a highest weight moudle. In this paper, we will determine the reducibility of such scalar type generalized Verma modules by computing the Gelfand-Kirillov dimension of L.

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