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arXiv · 1405.4167

Proper SL(2,R)-actions on homogeneous spaces

Maciej Bochenski·Piotr Jastrzebski·Takayuki Okuda·Aleksy Tralle
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Abstract

We study the existence problem of proper actions of SL(2,R) on homogeneous spaces G/H of reductive type. Based on Kobayashi's properness criterion [Math. Ann. (1989)], we show that G/H admits a proper SL(2,R)-action via G if a maximally split abelian subspace of Lie H is included in the wall defined by a restricted root of Lie G. We also give a number of examples of such G/H.

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Maciej Bochenski, Piotr Jastrzebski, Takayuki Okuda, Aleksy Tralle. 2016-10-27. Proper SL(2,R)-actions on homogeneous spaces. https://doi.org/10.1142/s0129167x16501068

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