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

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 Fsep\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F<^>{{{\,\textrm{sep}\,}}}$$\end{document} 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 in Shibata (J Algebra 547: 179-219, 2020).