Journal of Lie Theory 35 (2025), No. 4, 909--955
Copyright Heldermann Verlag 2025
Discrete Series Representations Decomposing Discretely with Finite Multiplicity under Restriction to Symmetric Subgroups
Bent Oersted
Mathematics Department, Aarhus University, Denmark
orsted@math.au.dk
Jorge A. Vargas
FAMAF-CIEM, Ciudad Universitaria, Córdoba, Argentina
vargas@famaf.unc.edu.ar
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 continue our study of the branching laws for Discrete Series when restricted to a subgroup H of the same type by use of integral and differential operators in combination with our previous duality principle. Many results are presented in generality, others are shown in detail for Holomorphic Discrete Series.
Keywords: Intertwining operators, admissible restriction, duality theorem, reproducing kernel, discrete series.
MSC: 22E46; 17B10.
[ Fulltext-pdf (327 KB)] for subscribers only.