Geodesic
Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III
Andreas Kriegl1 ; Mark Losik2 ; Peter W. Michor1, 3 ; Armin Rainer1
1Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria
2Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia
3und: Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, 1090 Wien, Austria
Journal of Lie Theory, Tome 16 (2006) no. 3, pp. 579-600

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22E45, 20F55
Mots-clés : Invariants, representations

Andreas Kriegl  1   ; Mark Losik  2   ; Peter W. Michor  1 , 3   ; Armin Rainer  1

1 Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria
2 Saratov State University, ul. Astrakhanskaya 83, 410026 Saratov, Russia
3 und: Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, 1090 Wien, Austria 
Andreas Kriegl; Mark Losik; Peter W. Michor; Armin Rainer. Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III. Journal of Lie Theory, Tome 16 (2006) no. 3, pp. 579-600. http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a9/
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     author = {Andreas Kriegl and Mark Losik and Peter W. Michor and Armin Rainer},
     title = {Lifting {Smooth} {Curves} over {Invariants} for {Representations} of {Compact} {Lie} {Groups,} {III}},
     journal = {Journal of Lie Theory},
     pages = {579--600},
     year = {2006},
     volume = {16},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a9/}
}
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