BRANCHING LAWS: SOME RESULTS AND NEW EXAMPLES

For a connected, noncompact simple matrix Lie group G so that a maximal compact subgroup K has a three dimensional simple ideal, in this note we analyze the admissibility of the restriction of irreducible square integrable representations for the ambient group when they are restricted to certain subgroups that contain the three dimensional ideal. In this setting we provide a formula for the multiplicity of the irreducible factors. Also, for general G such that G/K is an Hermitian G-manifold we give a necessary and sufficient condition so that an arbitrary square integrable representation of the ambient group is admissible over the semisimple factor of K.