Shapovalov determinants of Q-type Lie superalgebras

2005/11/25 by Maria Gorelik, Gorelik, Maria
Mathematics · Physics and Astronomy · #17B20 #17B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:17B20 #msc:17B35

paper · pdf · doi:10.48550/arxiv.math/0511623

60 pages

arxiv created 2005/11/25 · openalex publication_date 2005/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an analogue of Shapovalov forms for Q-type Lie superalgebras and factorize the corresponding Shapovalov determinants which are responsible for simplicity of highest weight modules. We apply the factorization to obtain a description of the centres of Q-type Lie superalgebras.

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