THE CONTINUOUS SPECTRUM IN DISCRETE SERIES BRANCHING LAWS

@article{Harris2012THECS,
  title={THE CONTINUOUS SPECTRUM IN DISCRETE SERIES BRANCHING LAWS},
  author={Benjamin Harris and Hongyu L. He and Gestur {\'O}lafsson},
  journal={International Journal of Mathematics},
  year={2012},
  volume={24},
  pages={1350049}
}
If G is a reductive Lie group of Harish-Chandra class, H is a symmetric subgroup, and π is a discrete series representation of G, the authors give a condition on the pair (G, H) which guarantees that the direct integral decomposition of π|H contains each irreducible representation of H with finite multiplicity. In addition, if G is a reductive Lie group of Harish-Chandra class, and H ⊂ G is a closed, reductive subgroup of Harish-Chandra class, the authors show that the multiplicity function in… 
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For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In this paper, we…

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