dc.contributor.author |
Bate, Michael |
en |
dc.contributor.author |
Martin, Benjamin |
en |
dc.contributor.author |
Röhrle, Gerhard |
en |
dc.date.accessioned |
2012-03-05T20:17:08Z |
en |
dc.date.issued |
2005 |
en |
dc.identifier.citation |
Inventiones Mathematicae 161(1):177-218 2005 |
en |
dc.identifier.issn |
0020-9910 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/12908 |
en |
dc.description.abstract |
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. |
en |
dc.publisher |
Springer-Verlag |
en |
dc.relation.ispartofseries |
Inventiones Mathematicae |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Detail obtained from http://www.sherpa.ac.uk/romeo/issn/0020-9910/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
A geometric approach to complete reducibility |
en |
dc.type |
Journal Article |
en |
dc.identifier.doi |
10.1007/s00222-004-0425-9 |
en |
pubs.issue |
1 |
en |
pubs.begin-page |
177 |
en |
pubs.volume |
161 |
en |
dc.rights.holder |
Copyright: Springer-Verlag |
en |
pubs.end-page |
218 |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
254377 |
en |
pubs.record-created-at-source-date |
2011-12-06 |
en |