## 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
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.