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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.01213 |
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| _version_ | 1866914368852066304 |
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| author | Kubo, Toshihisa |
| author_facet | Kubo, Toshihisa |
| contents | In this paper we classify and construct differential symmetry breaking operators $\mathbb{D}$ from a line bundle over the real projective space $\mathbb{R}\mathbb{P}^n$ to a vector bundle over $\mathbb{R}\mathbb{P}^{n-1}$. We further determine the factorization identities of $\mathbb{D}$ and the branching laws of the corresponding generalized Verma modules of $\mathfrak{sl}(n+1,\mathbb{C})$. By utilizing the factorization identities, the $SL(n,\mathbb{R})$-representations realized on the image $\text{Im}(\mathbb{D})$ are also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces Kubo, Toshihisa Representation Theory Differential Geometry 22E46, 17B10 In this paper we classify and construct differential symmetry breaking operators $\mathbb{D}$ from a line bundle over the real projective space $\mathbb{R}\mathbb{P}^n$ to a vector bundle over $\mathbb{R}\mathbb{P}^{n-1}$. We further determine the factorization identities of $\mathbb{D}$ and the branching laws of the corresponding generalized Verma modules of $\mathfrak{sl}(n+1,\mathbb{C})$. By utilizing the factorization identities, the $SL(n,\mathbb{R})$-representations realized on the image $\text{Im}(\mathbb{D})$ are also investigated. |
| title | Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces |
| topic | Representation Theory Differential Geometry 22E46, 17B10 |
| url | https://arxiv.org/abs/2408.01213 |