Cartan-decomposition subgroups of 𝑆𝑂(2,𝑛)

Oh, Hee; Morris, Dave

doi:10.1090/S0002-9947-03-03428-7

Cartan-decomposition subgroups of $\operatorname {SO}(2,n)$
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by Hee Oh and Dave Witte Morris PDF

Trans. Amer. Math. Soc. 356 (2004), 1-38 Request permission

Abstract:

For $G = \operatorname {SL} (3,\mathbb {R})$ 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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