Completely reducible SL(2)-homomorphisms

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dc.creatorMcNinch, George J.
dc.creatorTesterman, Donna M.
dc.date2005-10-18
dc.date.accessioned2026-07-07T09:39:29Z
dc.date.available2026-07-07T09:39:29Z
dc.descriptionLet 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.
dc.descriptionAMS LaTeX 20 pages
dc.identifierhttps://arxiv.org/abs/math/0510377
dc.identifierhttp://arxiv.org/abs/math/0510377
dc.identifierTransact. AMS 2007 (359) 4489-4510.
dc.identifierdoi:10.1090/S0002-9947-07-04289-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161186
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subjectGroup Theory
dc.subject20G15
dc.titleCompletely reducible SL(2)-homomorphisms
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