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1 December 2020 Branching problems in reproducing kernel spaces
Bent Ørsted, Jorge A. Vargas
Duke Math. J. 169(18): 3477-3537 (1 December 2020). DOI: 10.1215/00127094-2020-0032

Abstract

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.

Citation

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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

Information

Received: 19 June 2019; Revised: 28 February 2020; Published: 1 December 2020
First available in Project Euclid: 1 December 2020

MathSciNet: MR4181031
Digital Object Identifier: 10.1215/00127094-2020-0032

Subjects:
Primary: 22E46
Secondary: 17B10

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 18 • 1 December 2020
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