Branching problems in reproducing kernel spaces

Bent Ørsted, Jorge A. Vargas

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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 our work here 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 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.

Original languageEnglish
JournalDuke Mathematical Journal
Pages (from-to)3477-3537
Number of pages61
Publication statusPublished - 2020


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