Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III
Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 579-600
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.
@article{JOLT_2006_16_3_a9,
author = {A. Kriegl and M. Losik and P. W. Michor and A. 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},
doi = {10.5802/jolt.426},
zbl = {1112.22003},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.426/}
}
TY - JOUR AU - A. Kriegl AU - M. Losik AU - P. W. Michor AU - A. Rainer TI - Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III JO - Journal of Lie Theory PY - 2006 SP - 579 EP - 600 VL - 16 IS - 3 UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.426/ DO - 10.5802/jolt.426 ID - JOLT_2006_16_3_a9 ER -
%0 Journal Article %A A. Kriegl %A M. Losik %A P. W. Michor %A A. Rainer %T Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III %J Journal of Lie Theory %D 2006 %P 579-600 %V 16 %N 3 %U https://jolt.centre-mersenne.org/articles/10.5802/jolt.426/ %R 10.5802/jolt.426 %F JOLT_2006_16_3_a9
A. Kriegl; M. Losik; P. W. Michor; A. Rainer. Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III. Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 579-600. doi: 10.5802/jolt.426
Cited by Sources: