Reversibility properties of semigroup actions on homogeneous spaces (Q444687)

Let \(L\) be a subgroup of the connected non-contact semi-simple Lie group \(G\) with finite center. If \(S\) is a subsemigroup of \(G\) and acts on some space \(X\) one says that \(S\) is reversible in \(X\) in the cases when any two \(S\)-orbits in \(X\) have non-empty intersection. The main result of the paper gives necessary and sufficient conditions for a semigroup \(S \in G\) to be reversible in the homogeneous space \(G/L.\)