T. Kobayashi and B. Ørsted,
Conformal geometry and branching laws for unitary representations attached to minimal nilpotent orbits,
C. R. Acad. Sci. Paris 326 (1998), 925-930..

For the unitary representation of O(p,q) attached to the minimal nilpotent coadjoint orbit, we explicitly calculate its restriction to certain 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 orbits.
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