Journal of Lie Theory

no. 1
Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups
Journal of Lie Theory, Volume 24 (2014) no. 1, pp. 259-305
Let $G$ be a real semisimple Lie group with trivial centre and no compact factors. Given a conjugate pair of either real hyperbolic elements or unipotent elements $a$ and $b$ in $G$ we find a conjugating element $g \in G$ such that $d_G(1,g) \leq L(d_G(1,u)+d_G(1,v))$, where $L$ is a positive constant which will depend on some property of $a$ and $b$ (when $a,b$ are unipotent we require that the Lie algebra of $G$ is split). For the vast majority of such elements however, $L$ can be assumed to be a uniform constant.
DOI: 10.5802/jolt.784
Classification: 20F65, 20F10, 22E46, 53C35
Keywords: Geometric group theory, conjugacy problem, semisimple Lie groups 
@article{JOLT_2014_24_1_a11,
     author = {A. Sale},
     title = {Bounded {Conjugators} for {Real} {Hyperbolic} and {Unipotent} {Elements} in {Semisimple} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {259--305},
     year = {2014},
     volume = {24},
     number = {1},
     doi = {10.5802/jolt.784},
     zbl = {1311.22017},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.784/}
}
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%T Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups
%J Journal of Lie Theory
%D 2014
%P 259-305
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%N 1
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%R 10.5802/jolt.784
%F JOLT_2014_24_1_a11
A. Sale. Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups. Journal of Lie Theory, Volume 24 (2014) no. 1, pp. 259-305. doi: 10.5802/jolt.784

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