Super Vust theorem and Schur-Sergeev duality for principal finite W-superalgebras

2020/05/22 by Changjie Cheng, Cheng, Changjie, Bin Shu +3
Mathematics · #17B08 #17B10 #17B20 #81R05 #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.2005.11103

openalex publication_date 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Considering the general linear Lie superalgebra \mathfrakgl(m|n)=\mathfrakgl(m|n)_ 0⊕ \mathfrakgl(m|n)_ 1 over ℂ, we first formulate a super version of Vust theorem associated with a principal nilpotent element e∈ \mathfrakgl(m|n)_ 0. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite W-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in \citeBKl

Citations

• Finite W-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras
• The invariant theory of n × n matrices

Related

• Finite W-superalgebras for basic Lie superalgebras
• On a super-analog of the Schur-Weyl Duality
• Super duality for Whittaker modules and finite W-algebras
• Finite W-superalgebras for basic classical Lie superalgebras
• Levi-type Schur-Sergeev duality for general linear super groups