Abstract
For a semisimple Lie group satisfying the equal-rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In our work here we study some of the branching laws for discrete series when restricted to a subgroup of the same type by combining classical results with recent work of Kobayashi; in particular, we prove discrete decomposability under Harish-Chandra’s condition of cusp form on the reproducing kernel. We show a relation between discrete decomposability and representing certain intertwining operators in terms of differential operators.
Citation
Bent Ørsted. Jorge A. Vargas. "Branching problems in reproducing kernel spaces." Duke Math. J. 169 (18) 3477 - 3537, 1 December 2020. https://doi.org/10.1215/00127094-2020-0032
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