On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914556034416640 |
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| author | Pérez-Valdés, Víctor |
| author_facet | Pérez-Valdés, Víctor |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups Pérez-Valdés, Víctor Representation Theory Differential Geometry Primary 22E45, Secondary 58J70, 22E46, 22E47, 34A30 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. |
| title | On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups |
| topic | Representation Theory Differential Geometry Primary 22E45, Secondary 58J70, 22E46, 22E47, 34A30 |
| url | https://arxiv.org/abs/2506.23064 |