Containment Relations among Spherical Subgroups

A closed subgroup \(H\) of a connected reductive group \(G\) is called \(\textit{spherical}\) if a Borel subgroup in \(G\) has an open orbit on \(G/H\). We give a combinatorial characterization for a spherical subgroup to be contained in another one which generalizes previous work by Knop. As an application, we compute the Luna datum of the identity component of a spherical subgroup which yields a characterization of connectedness for spherical subgroups.