Proper SL(2,R)-actions on homogeneous spaces
Group Theory
2017-01-31 v3
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.
Keywords
Cite
@article{arxiv.1405.4167,
title = {Proper SL(2,R)-actions on homogeneous spaces},
author = {Maciej Bochenski and Piotr Jastrzebski and Takayuki Okuda and Aleksy Tralle},
journal= {arXiv preprint arXiv:1405.4167},
year = {2017}
}
Comments
to appear in International Journal of Mathematics