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Cartan-decomposition subgroups of
Authors:Hee Oh   Dave Witte Morris
Affiliation:Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078 ; Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Abstract:For $G = operatorname{SL} (3,mathord{mathbb{R} })$ and $G = operatorname{SO}(2,n)$, we give explicit, practical conditions that determine whether or not a closed, connected subgroup $H$of $G$ has the property that there exists a compact subset $C$ of $G$with $CHC = G$. To do this, we fix a Cartan decomposition $G = K A^+ K$of $G$, and then carry out an approximate calculation of $(KHK) cap A^+$for each closed, connected subgroup $H$ of $G$.

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