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References (17)
-
Universitätsstrasse 150, D-44780 Bochum, Germany E-mail address: gerhard.roehrle@rub -
A. Borel, R. Carter, C. Curtis, N. Iwahori, T. Springer, R. Steinberg (1970)
Seminar on Algebraic Groups and Related Finite Groups -
(2003)
Séminaire Bourbaki, 56ème année -
M. Bate, B. Martin, G. Röhrle (2004)
A geometric approach to complete reducibilityInventiones mathematicae, 161
-
B. Martin (2003)
A normal subgroup of a strongly reductive subgroup is strongly reductiveJournal of Algebra, 265
-
UK E-mail address: bate@maths.ox.ac.uk Mathematics and Statistics Department -
B. Martin (2003)
Reductive subgroups of reductive groups in nonzero characteristicJournal of Algebra, 262
-
T. Medts (2005)
LINEAR ALGEBRAIC GROUPS -
M. Liebeck, G. Seitz (1996)
Reductive subgroups of exceptional algebraic groups -
(1968)
Notes on Chevalley Groups -
George McNinch, D. Testerman (2007)
Completely reducible $\operatorname{SL}(2)$-homomorphismsTransactions of the American Mathematical Society, 359
-
R. Richardson (1982)
On orbits of algebraic groups and Lie groupsBulletin of the Australian Mathematical Society, 25
-
M. Bate, B. Martin, G. Röhrle, R. Tange (2007)
Complete reducibility and separabilityTransactions of the American Mathematical Society, 362
-
George McNinch, D. Testerman (2005)
Completely reducible (2)-homomorphismsTransactions of the American Mathematical Society, 359
-
(1998)
The notion of complete reducibility in group theory, Moursund Lectures -
M. Nagata (1961)
Complete reducibility of rational representations of a matric groupJournal of Mathematics of Kyoto University, 1
-
J. Jantzen (2004)
Nilpotent Orbits in Representation Theory
- Publisher
- de Gruyter
- Copyright
- © Walter de Gruyter Berlin · New York 2008
- ISSN
- 0075-4102
- eISSN
- 1435-5345
- DOI
- 10.1515/CRELLE.2008.063
- Publisher site
- See Article on Publisher Site
Abstract
Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p ≧ 0. We study J.-P. Serre's notion of G -complete reducibility for subgroups of G . Specifically, for a subgroup H and a normal subgroup N of H , we look at the relationship between G -complete reducibility of N and of H , and show that these properties are equivalent if H/N is linearly reductive, generalizing a result of Serre. We also study the case when H = MN with M a G -completely reducible subgroup of G which normalizes N . In our principal result we show that if G is connected, N and M are connected commuting G -completely reducible subgroups of G , and p is good for G , then H = MN is also G -completely reducible.
Journal
Journal für die reine und angewandte Mathematik (Crelle's Journal) – de Gruyter
Published: Aug 1, 2008