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arXiv · 2202.05138

Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank

Jose Carlos Diaz-Ramos·Miguel Dominguez-Vazquez·Tomas Otero
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Abstract

We develop a new structural result for cohomogeneity one actions on (not necessarily irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to classify cohomogeneity one actions on SL(n,R)/SO(n), n>1, up to orbit equivalence. We also reduce the classification problem on a reducible space to the classification on each one of its irreducible factors, which in particular allows to classify cohomogeneity one actions on any finite product of hyperbolic spaces.

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Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Tomas Otero. 2022-02-10. Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank. https://doi.org/10.1016/j.aim.2023.109165

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