Journal of Lie Theory 16 (2006), No. 3, 579--600
Copyright Heldermann Verlag 2006
Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III
Andreas Kriegl
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria
Andreas.Kriegl@univie.ac.at
Mark Losik
Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia
losikMV@info.sgu.ru
Peter W. Michor
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria
und: Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, 1090 Wien, Austria
Peter.Michor@esi.ac.at
Armin Rainer
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria
armin.rainer@univie.ac.at
Any sufficiently often differentiable curve in the orbit space V/G of a real finite dimensional orthogonal representation G to O(V) of a finite group G admits a differentiable lift into the representation space V with locally bounded derivative. As a consequence any sufficiently often differentiable curve in the orbit space V/G can be lifted twice differentiably which is in general best possible. These results can be generalized to arbitrary polar representations. Finite reflection groups and finite rotation groups in dimensions two and three are discussed in detail.
Keywords: Invariants, representations.
MSC: 22E45, 20F55
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