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

Lukas Bonfert; Jonas Nehme

doi:10.1016/j.jalgebra.2023.12.004

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arXiv · 2305.04751

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

Lukas Bonfert·Jonas Nehme

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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 $\mathfrak{sl}(m|n)$, $\mathfrak{osp}(2m+1|2n)$ and $\mathfrak{osp}(2m|2n)$ we explicitly describe the Cartan graph in terms of partitions and determine the relations between the generators of their Weyl groupoids.

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Lukas Bonfert, Jonas Nehme. 2023-05-08. The Weyl groupoids of $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(r|2n)$. https://doi.org/10.1016/j.jalgebra.2023.12.004

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