Unitary branching rules for the general linear Lie superalgebra

2024/10/07 by M. D. Gould, Yang Zhang, Gould, Mark +1
Mathematics · Physics and Astronomy · #05E10 #17B10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.04902

openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In terms of highest weights, we establish branching rules for finite dimensional unitary simple modules of the general linear Lie superalgebra \mathfrakgl_m|n. Our proof uses the Howe duality for \mathfrakgl_m|n, as well as branching rules for Kac modules. Moreover, we derive the branching rules of type 2 unitary simple \mathfrakgl_m|n-modules, which are dual to the aforementioned unitary modules.

Related

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• Howe Duality for Lie Superalgebras