Construction and classification of differential symmetry breaking operators for principal series representations of the pair $(SO_0(4,1), SO_0(3,1))$ for special parameters
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913078273114112 |
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| author | Pérez-Valdés, Víctor |
| author_facet | Pérez-Valdés, Víctor |
| contents | We construct and give a complete classification of all the differential symmetry breaking operators $\mathbb{D}_{λ, ν}^{N,m}: C^\infty(S^3, \mathcal{V}_λ^{2N+1}) \rightarrow C^\infty(S^2, \mathcal{L}_{m, ν})$, between the spaces of smooth sections of a vector bundle of rank $2N+1$ over the $3$-sphere $\mathcal{V}_λ^{2N+1} \rightarrow S^3$, and a line bundle over the $2$-sphere $\mathcal{L}_{m, ν} \rightarrow S^2$ in the special case $|m| = N$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_01977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction and classification of differential symmetry breaking operators for principal series representations of the pair $(SO_0(4,1), SO_0(3,1))$ for special parameters Pérez-Valdés, Víctor Representation Theory 22E45, 58J70, 22E46, 22E47, 34A30 We construct and give a complete classification of all the differential symmetry breaking operators $\mathbb{D}_{λ, ν}^{N,m}: C^\infty(S^3, \mathcal{V}_λ^{2N+1}) \rightarrow C^\infty(S^2, \mathcal{L}_{m, ν})$, between the spaces of smooth sections of a vector bundle of rank $2N+1$ over the $3$-sphere $\mathcal{V}_λ^{2N+1} \rightarrow S^3$, and a line bundle over the $2$-sphere $\mathcal{L}_{m, ν} \rightarrow S^2$ in the special case $|m| = N$. |
| title | Construction and classification of differential symmetry breaking operators for principal series representations of the pair $(SO_0(4,1), SO_0(3,1))$ for special parameters |
| topic | Representation Theory 22E45, 58J70, 22E46, 22E47, 34A30 |
| url | https://arxiv.org/abs/2504.01977 |