On the Duflo-Serganova functor for the queer Lie superalgebra

Maria Gorelik; Alexander Sherman

On the Duflo-Serganova functor for the queer Lie superalgebra

Representation Theory 2022-05-03 v2

Authors: Maria Gorelik , Alexander Sherman

Abstract

We study the Duflo-Serganova functor $\operatorname{DS}_x$ for the queer Lie superalgebra $\mathfrak{q}_n$ 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 $\lambda$ . Further, we prove that $\operatorname{DS}_x(L)$ is semisimple if $L$ is a simple finite-dimensional module and $x$ is of rank $1$ satisfying $x^2=0$ .

Keywords

duflo-serganova functor queer lie superalgebra odd elements arc diagram semisimple modules finite-dimensional modules

Cite

@article{arxiv.2204.05048,
  title  = {On the Duflo-Serganova functor for the queer Lie superalgebra},
  author = {Maria Gorelik and Alexander Sherman},
  journal= {arXiv preprint arXiv:2204.05048},
  year   = {2022}
}

Comments

33 pages; for $DS_x$ with $x$ is of rank 1 and $x^2=0$: computed grading, and proved it is semisimple functor; other minor changes made

On the Duflo-Serganova functor for the queer Lie superalgebra

Abstract

Keywords

Cite

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