Reducible subgroups of exceptional algebraic groups |
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Authors: | Alastair J. Litterick Adam R. Thomas |
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Affiliation: | 1. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, D-44780 Bochum, Germany;2. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany;3. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK;4. The Heilbronn Institute for Mathematical Research, Bristol, UK |
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Abstract: | Let G be a simple algebraic group over an algebraically closed field. A closed subgroup H of G is called G-completely reducible (G-cr) if, whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi factor of P. In this paper we complete the classification of connected G-cr subgroups when G has exceptional type, by determining the -irreducible connected reductive subgroups for each simple classical factor of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type and various properties thereof. This work complements results of Lawther, Liebeck, Seitz and Testerman, and is vital in classifying non-G-cr reductive subgroups, a project being undertaken by the authors elsewhere. |
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Keywords: | Primary 20G07 secondary 20G41 20G10 |
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