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arXiv · 2309.15967

Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms

Takuma Hayashi
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Abstract

In this paper, we classify irreducible representations of affine group superschemes over fields $F$ of characteristic not two in terms of those over a separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute the division superalgebras of their endomorphisms. Finally, we give numerical conclusions for quasi-reductive algebraic supergroups under certain conditions, based on Shibata's Borel--Weil theory for split quasi-reductive algebraic supergroups.

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BibTeXRIS

Takuma Hayashi. 2023-09-27. Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms. https://doi.org/10.1007/s00209-024-03664-9

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