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- W1970665890 abstract "Let $K$ be any field, and let $G$ be a semisimple group over $K$. Suppose the characteristic of $K$ is positive and is very good for $G$. We describe all group scheme homomorphisms $phi :operatorname {SL}_2 to G$ whose image is geometrically $G$-completely reducibleâor $G$-crâin the sense of Serre; the description resembles that of irreducible modules given by Steinbergâs tensor product theorem. In case $K$ is algebraically closed and $G$ is simple, the result proved here was previously obtained by Liebeck and Seitz using different methods. A recent result shows the Lie algebra of the image of $phi$ to be geometrically $G$-cr; this plays an important role in our proof." @default.
- W1970665890 created "2016-06-24" @default.
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- W1970665890 date "2007-09-01" @default.
- W1970665890 modified "2023-09-27" @default.
- W1970665890 title "Completely reducible $operatorname{SL}(2)$-homomorphisms" @default.
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- W1970665890 doi "https://doi.org/10.1090/s0002-9947-07-04289-4" @default.
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