Branching problems in reproducing kernel spaces

@article{Orsted2019BranchingPI,
  title={Branching problems in reproducing kernel spaces},
  author={Bent Orsted and Jorge Antonio Vargas},
  journal={arXiv: Representation Theory},
  year={2019}
}
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 study some of the branching laws for discrete series when restricted to a subgroup $H$ of the same type by combining classical results with recent work of T. Kobayashi; in particular, we prove discrete decomposability under Harish-Chandra's condition of cusp form on the reproducing kernel. We show a… 
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