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

Liu, Gang; Oshima, Yoshiki; Yu, Jun

doi:10.1090/ert/658

Restriction of irreducible unitary representations of $\operatorname {Spin}(N,1)$ to parabolic subgroups
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by Gang Liu, Yoshiki Oshima and Jun Yu;

Represent. Theory 27 (2023), 887-932

DOI: https://doi.org/10.1090/ert/658

Published electronically: September 21, 2023

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Abstract:

In this paper, we obtain explicit branching laws for all irreducible unitary representations of $G=\operatorname {Spin}(N,1)$ when restricted to a parabolic subgroup $P$. 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.

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