## Proper actions of $SL(2,\mathbb{R})$ on $SL(n,\mathbb{R})$ -- homogeneous spaces

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 1, Page 1--13.

Teduka, Katsuki
Proper actions of $SL(2,\mathbb{R})$ on $SL(n,\mathbb{R})$ -- homogeneous spaces
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
This paper gives a necessary and sufficient condition for the homogeneous spaces of $SL(n,\mathbb{R})$ to admit proper actions of $SL(2,\mathbb{R})$, or equivalently, to admit an infinite discontinuous group generated by a unipotent element. The method of our proof is based on Kobayashi's criterion for proper actions on homogeneous spaces of reductive type.

Keywords: proper action, homogeneous space, reductive group, properly discontinuous action, Fuchs group

Mathematics Subject Classification (2000): Primary 22F30; Secondary 22E40, 53C30, 53C35, 57S30
Mathematical Reviews Number: MR2422587