A geometric approach to complete reducibility
By M. Bate, B. Martin, G. Röhrle. 2004
99 citations recorded by the source corpus.
Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert–Mumford–Kempf from geometric invariant theory. We deduce that a normal subgroup of a G-completely reducible subgroup of G is again G-completely reducible, thereby providing an affirmative answer to a question posed by J.-P. Serre, and conversely we prove that the normalizer of a G-completely reducible subgroup of G is again G-completely reducible. Some rationality questions and applications to the spherical building of G are considered. Many of our results extend to the case of non-connected G.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1cceb35f977e1c16d8e801803edddb63f30c02cc
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In Discrete Mathematics and Combinatorics
In Mathematical Physics
Citations in the corpus
- On the Smoothness of Centralizers in Reductive Groups (2010, result): “ infinitesimal fixed points of Hin Lie(G). Here, in contrast to the later sections of the paper, we do not consider scheme-theoretic centralizers. A similar notion exists for subalgebras of Lie(G). See [BMR05] and [BMRT] for these concepts and their importance in the context of Serre’s notion of G-com”