Journal of Lie Theory Vol. 12, No. 1, pp. 191203 (2002) 

On Orbit Dimensions under a Simultaneous Lie Group Action on n Copies of a ManifoldMireille BoutinMireille Boutin127 Vincent Hall 206 Church Street S.E. Minneapolis, MN 55455 mboutin@math.umn.edu Abstract: We show that the maximal orbit dimension of a simultaneous Lie group action on $n$ copies of a manifold does not pseudostabilize when $n$ increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then the induced Cartesian action is locally free on an open and dense subset of a sufficiently big (but finite) number of copies of the manifold. The latter is the analogue for the Cartesian action to OlverOvsiannikov's theorem on jet bundles and is an important fact relative to the moving frame method and the computation of joint invariants. Some interesting corollaries are presented. Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
