PreprintCC BY 4.0arXiv
Symmetry breaking differential operators and Discrete Series
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 study the structure of symmetry breaking operators for Discrete Series when restricted to a subgroup H of the same type by combining classical results with recent work of T. Kobayashi, Nakahama and Pevzner. This we do by using reproducing kernels for the representations and our previous duality principle in order to find some explicit details on the nature of the differential operators representing symmetry breaking operators, in particular to what extent they are given by differentiations in normal directions to the H-orbit in G/K.
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BibTeX
@misc{orsted2026symmetry,
title = {{Symmetry breaking differential operators and Discrete Series}},
author = {Bent Ørsted and Jorge A. Vargas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19082},
eprint = {2609.19082},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19082},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry breaking differential operators and Discrete Series
AU - Bent Ørsted
AU - Jorge A. Vargas
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19082
UR - https://arxiv.org/abs/2609.19082
AB - 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 study the structure of symmetry breaking operators for Discrete Series when restricted to a subgroup H of the same type by combining classical results with recent work of T. Kobayashi, Nakahama and Pevzner. This we do by using reproducing kernels for the representations and our previous duality principle in order to find some explicit details on the nature of the differential operators representing symmetry breaking operators, in particular to what extent they are given by differentiations in normal directions to the H-orbit in G/K.
ER -