Semisimplicity of the DS functor for the orthosymplectic Lie\n superalgebra

2020/10/28 by Maria Gorelik, Gorelik, Maria, Thorsten Heidersdorf +1
Mathematics · #17B10 #17B20 #17B55 #18D10 #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.2010.14975

openalex publication_date 2020/10/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We prove that the Duflo-Serganova functor DS_x attached to an odd nilpotent\nelement x of mathfrakosp(m|2n) is semisimple, i.e. sends a semisimple\nrepresentation M of mathfrakosp(m|2n) to a semisimple representation of\n mathfrakosp(m-2k|2n-2k) where k is the rank of x. We prove a closed\nformula for DS_x(L(\λ)) in terms of the arc diagram attached to\n\λ.\n

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