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

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.

Final version. Minor typos were corrected. To appear in Mathematische Zeitschrift

References in corpus (3)

• A new proof of the Mullineux conjecture
• Half-integrality of line bundles on partial flag schemes of classical Lie groups
• Real forms of complex Lie superalgebras and supergroups

Cited by in corpus (1)

• Rationality patterns