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On orbits of algebraic groups and Lie groups

Published online by Cambridge University Press:  17 April 2009

R.W. Richardson
R.W. Richardson
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, PO Box 4, Canberra, ACT 2600, Australia.
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Abstract

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In this paper we will be concerned with orbits of a closed subgroup Z of an algebraic group (respectively Lie group) G on a homogeneous space X for G. More precisely, let D be a closed subgroup of G and let X denote the coset space G/D. Let S be a subgroup of G and let Z denote (GS)0 the identity component of GS, the centralizer of S in G. We consider the orbits of Z on XS, the set of fixed points of S on X. We also treat the more general situation in which S is an algebraic group (respectively Lie group) which acts on G by automorphisms and acts on X compatibly with the action of G; again we consider the orbits of (GS)0 on XS.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 1 - 28
Copyright
Copyright © Australian Mathematical Society 1982

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