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arXiv · 1301.0489

Decomposition Theorems for Triple Spaces

Thomas Danielsen·Bernhard Krötz·Henrik Schlichtkrull
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Abstract

A triple space is a homogeneous space $G/H$ where $G=G_0\times G_0\times G_0$ is a threefold product group and $H\simeq G_0$ the diagonal subgroup of $G$. This paper concerns the geometry of the triple spaces with $G_0=\SL(2,\R)$, $\SL(2,\C)$ or $\SO_e(n,1)$ for $n\ge 2$. We determine the abelian subgroups $A\subset G$ for which there is a polar decomposition $G=KAH$, and we determine for which minimal parabolic subgroups $P\subset G$, the orbit $PH$ is open in $G/H$.

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Thomas Danielsen, Bernhard Krötz, Henrik Schlichtkrull. 2013-01-03. Decomposition Theorems for Triple Spaces. https://doi.org/10.1007/s10711-014-0008-x

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