CONFORMAL GEOMETRY AND BRANCHING LAWS FOR UNITARY REPRESENTATIONS ATTACHED TO MINIMAL NILPOTENT ORBITS

For the unitary representation of O(p, q) attached to the minimal nilp otent coadjoint orbit, we explicitly calculate its restriction to cert ain natural dual pairs in O(p, q). We furthermore show how the results are compatible with the orbit method, in particular when viewing the minimal nilpotent orbit as belonging to the limit set of semisimple or bits. (C) Academie des Sciences/Elsevier, Paris.