Knop F, Röhrle G (2015)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2015
Publisher: Springer Verlag (Germany) / Foundation Compositio Mathematica
Book Volume: 151
Pages Range: 1288-1308
Journal Issue: 7
DOI: 10.1112/80010437X1400791X
Let G be a simple algebraic group. A closed subgroup H of G is said to be spherical if it has a dense orbit on the flag variety G/B of G. Reductive spherical subgroups of simple Lie groups were classified by Kramer in 1979. In 1997, Brundan showed that each example from Kramer's list also gives rise to a spherical subgroup in the corresponding simple algebraic group in any positive characteristic. Nevertheless, up to now there has been no classification of all such instances in positive characteristic. The goal of this paper is to complete this classification. It turns out that there is only one additional instance (up to isogeny) in characteristic 2 which has no counterpart in Kramer's classification. As one of our key tools, we prove a general deformation result for subgroup schemes that allows us to deduce the sphericality of subgroups in positive characteristic from the same property for subgroups in characteristic zero.
APA:
Knop, F., & Röhrle, G. (2015). Spherical subgroups in simple algebraic groups. Compositio Mathematica, 151(7), 1288-1308. https://doi.org/10.1112/80010437X1400791X
MLA:
Knop, Friedrich, and Gerhard Röhrle. "Spherical subgroups in simple algebraic groups." Compositio Mathematica 151.7 (2015): 1288-1308.
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