English

The Weyl groupoids of $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(r|2n)$

Representation Theory 2024-01-15 v2 Rings and Algebras

Abstract

We provide a convenient formulation of the definition of Cartan graphs and Weyl groupoids introduced by Heckenberger and Schneider, and construct Cartan graphs for regular symmetrizable contragredient Lie superalgebras. For sl(mn)\mathfrak{sl}(m|n), osp(2m+12n)\mathfrak{osp}(2m+1|2n) and osp(2m2n)\mathfrak{osp}(2m|2n) we explicitly describe the Cartan graph in terms of partitions and determine the relations between the generators of their Weyl groupoids.

Keywords

Cite

@article{arxiv.2305.04751,
  title  = {The Weyl groupoids of $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(r|2n)$},
  author = {Lukas Bonfert and Jonas Nehme},
  journal= {arXiv preprint arXiv:2305.04751},
  year   = {2024}
}