Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

2018/07/10 by Chih-Whi Chen, Chen, Chih-Whi, Kevin Coulembier +3 · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1807.03834

openalex publication_date 2018/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the tensor product of a simple and a finite dimensional \mathfraksl_n-module has finite type socle. This is applied to reduce classification of simple \mathfrakq(n)-supermodules to that of simple \mathfraksl_n-modules. Rough structure of simple \mathfrakq(n)-supermodules, considered as \mathfraksl_n-modules, is described in terms of the combinatorics of category O.

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• Categorification of generic Su-Zhang character formula
• \mathfrak b₁-Verma \mathfrak b₂-dual Verma supermodules
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