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Journal of Lie Theory 24 (2014), No. 1, 259--305
Copyright Heldermann Verlag 2014

Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups

Andrew Sale
IRMAR, Université de Rennes 1, 263 avenue du Général Leclerc, CS 74205, 35042 Rennes, France


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.

Keywords: Geometric group theory, conjugacy problem, semisimple Lie groups.

MSC: 20F65, 20F10, 22E46, 53C35

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