Preprint Series 2009 / 2010 No : 11 Title : ‘ Complete Reducibility and Separable Field Extensions ’ Author ( S )
نویسندگان
چکیده
Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies on the recently established Tits Centre Conjecture for the spherical building of the reductive group G.
منابع مشابه
No : 1 Title : ‘ Closed Orbits and Uniform S - Instability in Geometric Invariant Theory
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 S...
متن کاملClosed Orbits and Uniform S-instability in Invariant Theory
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 S...
متن کاملComplete Reducibility and Separability
Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre’s concept of Gcomplete reducibility for subgroups of G. A separability hypothesis appears in many general th...
متن کاملPREPRINT SERIES 2010 / 2011 NO : 18 TITLE : ‘ YANGIANS , S - MATRICES AND AdS / CFT ’ AUTHOR ( S )
This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected i...
متن کاملOn the Complexity of the Uniform Homeomorphism Relation between Separable Banach Spaces
Recently, there has been a growing interest in understanding the complexity of common analytic equivalence relations between separable Banach spaces via the notion of Borel reducibility in descriptive set theory (see [Bos] [FG] [FLR] [FR1] [FR2] [Me]). In general, the notion of Borel reducibility yields a hierarchy (though not linear) among equivalence relations in terms of their relative compl...
متن کامل