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arXiv · 2010.14975

Semisimplicity of the $DS$ functor for the orthosymplectic Lie superalgebra

Maria Gorelik·Thorsten Heidersdorf
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Abstract

We prove that the Duflo-Serganova functor $DS_x$ attached to an odd nilpotent element $x$ of $\mathfrak{osp}(m|2n)$ is semisimple, i.e. sends a semisimple representation $M$ of $\mathfrak{osp}(m|2n)$ to a semisimple representation of $\mathfrak{osp}(m-2k|2n-2k)$ where $k$ is the rank of $x$. We prove a closed formula for $DS_x(L(\lambda))$ in terms of the arc diagram attached to $\lambda$.

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Maria Gorelik, Thorsten Heidersdorf. 2020-10-28. Semisimplicity of the $DS$ functor for the orthosymplectic Lie superalgebra. https://arxiv.org/abs/2010.14975

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