T. Kobayashi,

*Criterion for proper actions on homogeneous spaces of reductive
groups*,

J. Lie Theory**6** (1996),
no. 2, 147-163..

J. Lie Theory

Let[ JLT | ZMath | related paper ]Mbe a manifold, on which a real reductive Lie groupGacts transitively. The action of a discrete subgroup Γ onMis not always properly discontinuous. In this paper, we give a criterion for properly discontinuous actions, which generalizes our previous work [6] for an analogous problem in the continuous setting. Furthermore, we introduce the discontinuous dual \pitchfork (H:G) of a subsetHofG, and prove a duality theorem that each subsetHofGis uniquely determined by its discontinuous dual up to multiplication by compact subsets.

© Toshiyuki Kobayashi