Completely reducible SL(2)-homomorphisms

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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:SL(2) --> G whose image is geometrically G-completely reducible -- or G-cr -- in the sense of Serre; the description resembles that of irreducible modules given by Steinberg's 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.
AMS LaTeX 20 pages

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Representation Theory, Algebraic Geometry, Group Theory, 20G15

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http://salesiana.dossiersoluciones.com/handle/123456789/161186

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510377
 http://arxiv.org/abs/math/0510377
 Transact. AMS 2007 (359) 4489-4510.
 doi:10.1090/S0002-9947-07-04289-4

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arXiv