Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad

We consider irreducible unitary representations $A_i$ of G=SO(n+1,1) with the same infinitesimal character as the trivial representation and representations $B_j$ of H=SO(n,1) with the same properties and discuss H-equivariant homomorphisms Hom_H($A_i,B_j$). For tempered representations our results confirm the predictions of conjectures by B. Gross and D. Prasad.