Restriction of irreducible unitary representations of 𝑆𝑝𝑖𝑛(𝑁,1) to parabolic subgroups

Abstract

In this paper, we obtain explicit branching laws for all irreducible unitary representations of G = Spin ⁡ ( N , 1 ) G=\operatorname {Spin}(N,1) when restricted to a parabolic subgroup P P . The restriction turns out to be a finite direct sum of irreducible unitary representations of P P . We also verify Duflo’s conjecture for the branching laws of discrete series representations of G G with respect to P 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.