RESTRICTION OF IRREDUCIBLE UNITARY REPRESENTATIONS OF Spin(N, 1) TO PARABOLIC SUBGROUPS

In this paper, we obtain explicit branching laws for all irreducible unitary representations of G = Spin(N, 1) when restricted to a parabolic sub-group P. The restriction turns out to be a finite direct sum of irreducible unitary representations of P. We also verify Duflo's conjecture for the branching laws of discrete series representations of G with respect to P. That is to show: in the framework of the orbit method, the branching law of a discrete series representation is determined by some geometric behavior of the moment map for the corresponding coadjoint orbit.