Discrete Series Representations Decomposing Discretely with Finite Multiplicity under Restriction to Symmetric Subgroups

B. Oersted; J. A. Vargas

doi:10.5802/jolt.1413

B. Oersted; J. A. Vargas

Journal of Lie Theory, Volume 35 (2025) no. 4, pp. 909-955

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 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.

Zbl

DOI: 10.5802/jolt.1413

Classification: 22E46, 17B10
Keywords: Intertwining operators, admissible restriction, duality theorem, reproducing kernel, discrete series

@article{JOLT_2025_35_4_a9,
     author = {B. Oersted and J. A. Vargas},
     title = {Discrete {Series} {Representations} {Decomposing} {Discretely} with {Finite} {Multiplicity} under {Restriction} to {Symmetric} {Subgroups}},
     journal = {Journal of Lie Theory},
     pages = {909--955},
     year = {2025},
     volume = {35},
     number = {4},
     doi = {10.5802/jolt.1413},
     zbl = {08124776},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1413/}
}

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B. Oersted; J. A. Vargas. Discrete Series Representations Decomposing Discretely with Finite Multiplicity under Restriction to Symmetric Subgroups. Journal of Lie Theory, Volume 35 (2025) no. 4, pp. 909-955. doi: 10.5802/jolt.1413

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