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.

Automated summary

This paper obtains explicit branching laws for all irreducible unitary representations of G = Spin(N,1) when restricted to a parabolic subgroup P. The results show that the restriction is a finite direct sum of irreducible unitary representations of P. The paper also verifies Duflo's conjecture for the branching laws of discrete series representations of G with respect to P, which states that the branching law of a discrete series representation is determined by some geometric behavior of the moment map for the corresponding coadjoint orbit in the framework of the orbit method.