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CLOSED ORBITS AND UNIFORM S-INSTABILITY IN INVARIANT THEORY

By Michael Bate, Benjamin Martin, Gerhard Röhrle and Rudolf Tange

Abstract

Abstract. In this paper we consider various problems involving the action of a reductive group G on an affine variety V. We prove some general rationality results about the G-orbits in V. In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of G for such general G-actions. We apply our general rationality results to answer a question of Serre concerning how his notion of G-complete reducibility behaves under separable field extensions. Applications of our new optimality results also include a construction which allows us to associate an optimal destabilizing parabolic subgroup of G to any subgroup of G. Finally, we use these new optimality techniques to provide an answer to Tits ’ Centre Conjecture in a special case

Topics: Contents
Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.192.4110
Provided by: CiteSeerX
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