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

Maria Gorelik; Thorsten Heidersdorf

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

Representation Theory 2020-10-29 v1

Authors: Maria Gorelik , Thorsten Heidersdorf

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 $\lambda$ .

Keywords

duflo-serganova functor orthosymplectic lie superalgebra semisimple representation odd nilpotent element arc diagram

Cite

@article{arxiv.2010.14975,
  title  = {Semisimplicity of the $DS$ functor for the orthosymplectic Lie superalgebra},
  author = {Maria Gorelik and Thorsten Heidersdorf},
  journal= {arXiv preprint arXiv:2010.14975},
  year   = {2020}
}

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