Mathematics – Representation Theory
Scientific paper
2005-04-06
J. Lie Theory 16 (2006), 579--600
Mathematics
Representation Theory
19 pages, Latex
Scientific paper
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. 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.
Kriegl Andreas
Losik Mark
Michor Peter W.
Rainer Armin
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