2024/11/26 by Yang Luo, Yongjie Wang, Luo, Yang +1 · 1 citation
Mathematics · #(2020): 17B35 #17B10 #20C30 #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.2411.17093
openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we provide a comprehensive characterization of invariants of classical Lie superalgebras from the super-analog of the Schur-Weyl duality in a unified way. We establish \mathfrakg-invariants of the tensor algebra T(\mathfrakg), the supersymmetric algebra S(\mathfrakg), and the universal enveloping algebra U(\mathfrakg) of a classical Lie superalgebra \mathfrakg corresponding to every element in centralizer algebras and their relationship under supersymmetrization. As a byproduct, we prove that the restriction on T(\mathfrakg)^\mathfrakg of the projection from T(\mathfrakg) to U(\mathfrakg) is surjective, which enables us to determine the generators of the center Z(\mathfrakg) except for \mathfrakg=\mathfrakosp2m|2n. Additionally, we present an alternative algebraic proof of the triviality of Z(\mathfrakpn). The key ingredient involves a technique lemma related to the symmetric group and Brauer diagrams.