On the Duflo-Serganova functor for the queer Lie superalgebra

2022/04/11 by Maria Gorelik, Gorelik, Maria, Alexander Sherman +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2204.05048

openalex publication_date 2022/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Duflo-Serganova functor DS_x for the queer Lie superalgebra \mathfrakq_n and for all odd x with [x,x] semisimple. For the case when the rank of x is 1 we give a formula for multiplicities in terms of the arc diagram attached to λ. Further, we prove that DS_x(L) is semisimple if L is a simple finite-dimensional module and x is of rank 1 satisfying x²=0.

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