Borel-Weil theorem for algebraic supergroups (Q2285227)

The paper under review proposes a framework for characteristic-free study of the representation theory of a quasi-reductive supergroup \(\mathbb{G}\). The first main result is an analogue of the Borel-Weil theorem, it provides a systematic construction of all simple \(\mathbb{G}\)-supermodules in arbitrary characteristic. The second main result of the paper treats the case when \(\mathbb{G}\) has a distinguished parabolic supersubgroup. In this case it is shown that the set of all simple \(\mathbb{G}\)-supermodules can be parameterized by the set of all dominant weights for the even part of \(\mathbb{G}\). Additionally, an analogue of Kempf's vanishing theorem is obtained.