Journal of Lie Theory 27 (2017), No. 4, 1033--1056
Copyright Heldermann Verlag 2017
Square Integrable Representations of Reductive Lie Groups with Admissible Restriction to SL2(R)
Michel Duflo
UFR de Mathématiques, Université Paris 7 - Diderot, IMJ-PRG / Case 7012, 75205 Paris Cedex 13, France
michel.duflo@imj-prg.fr
Esther Galina
FaMAF-CIEM, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentine
galina@famaf.unc.edu.ar
Jorge A. Vargas
FaMAF-CIEM, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentine
vargas@famaf.unc.edu.ar
We determine the irreducible square integrable representations of a reductive connected Lie group which admit an H-admissible restriction to a subgroup H locally isomorphic to SL2(R). We show that such a representation is holomorphic and we determine the essentially unique H with this property as well as multiplicity formulae.
Keywords: Discrete Series, branching laws, admissible restriction.
MSC: 22E46; 17B10
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