2024/08/15 by Zhanqiang Bai, Jing Jiang, Bai, Zhanqiang +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2408.07951
openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a Hermitian type Lie group with maximal compact subgroup K. Let L(λ) be a highest weight Harish-Chandra module of G with the infinitesimal character λ. By using some combinatorial algorithm, we obtain a description of the annihilator variety of L(λ). As an application, when L(λ) is unitarizable, we prove that the Gelfand-Kirillov dimension of L(λ) only depends on the value of z=(λ,β\vee), where β is the highest root.