On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups

[2506.23064] On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Representation Theory arXiv:2506.23064 (math) [Submitted on 29 Jun 2025 ( v1 ), last revised 12 May 2026 (this version, v5)] Title: On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups Authors: Víctor Pérez-Valdés View a PDF of the paper titled On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups, by V\'ictor P\'erez-Vald\'es View PDF HTML (experimental) Abstract: In this paper, we construct and classify all differential symmetry breaking operators between certain principal series representations of the pair $SO_0(4,1) \supset SO_0(3,1)$. In this case, we also prove a localness theorem, namely, all symmetry breaking operators between the principal series representations in concern are necessarily differential operators. In addition, we show that all these symmetry breaking operators are sporadic in the sense of T. Kobayashi, that is, they cannot be obtained by residue formulas of meromorphic families of symmetry breaking operators. Comments: 56 pages, 5 figures Subjects: Representation Theory (math.RT) ; Differential Geometry (math.DG) MSC classes: Primary 22E45, Secondary 58J70, 22E46, 22E47, 34A30 Cite as: arXiv:2506.23064 [math.RT] (or arXiv:2506.23064v5 [math.RT] for this version) https://doi.org/10.48550/arXiv.2506.23064 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Víctor Pérez-Valdés [ view email ] [v1] Sun, 29 Jun 2025 02:43:37 UTC (407 KB) [v2] Fri, 16 Jan 2026 06:08:38 UTC (405 KB) [v3] Sun, 8 Mar 2026 05:49:11 UTC (405 KB) [v4] Fri, 10 Apr 2026 05:50:12 UTC (405 KB) [v5] Tue, 12 May 2026 02:54:08 UTC (405 KB) Full-text links: Access Paper: View a PDF of the paper titled On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups, by V\'ictor P\'erez-Vald\'es View PDF HTML (experimental) TeX Source view license Current browse context: math.RT < prev | next > new | recent | 2025-06 Change to browse by: math math.DG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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