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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2312.15621 |
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| _version_ | 1866916357770051584 |
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| author | Kubo, Toshihisa Ørsted, Bent |
| author_facet | Kubo, Toshihisa Ørsted, Bent |
| contents | We classify and construct $SL(n,\mathbb{R})$-intertwining differential operators $\mathcal{D}$ from a line bundle to a vector bundle over the real projective space $\mathbb{RP}^{n-1}$ by the F-method. This generalizes a classical result of Bol for $SL(2,\mathbb{R})$. Further, we classify the $K$-type formulas for the kernel $\text{Ker}(\mathcal{D})$ and image $\text{Im}(\mathcal{D})$ of $\mathcal{D}$. The standardness of the homomorphisms $φ$ corresponding to the differential operators $\mathcal{D}$ between generalized Verma modules are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the intertwining differential operators from a line bundle to a vector bundle over the real projective space Kubo, Toshihisa Ørsted, Bent Representation Theory Differential Geometry 22E46, 17B10 We classify and construct $SL(n,\mathbb{R})$-intertwining differential operators $\mathcal{D}$ from a line bundle to a vector bundle over the real projective space $\mathbb{RP}^{n-1}$ by the F-method. This generalizes a classical result of Bol for $SL(2,\mathbb{R})$. Further, we classify the $K$-type formulas for the kernel $\text{Ker}(\mathcal{D})$ and image $\text{Im}(\mathcal{D})$ of $\mathcal{D}$. The standardness of the homomorphisms $φ$ corresponding to the differential operators $\mathcal{D}$ between generalized Verma modules are also discussed. |
| title | On the intertwining differential operators from a line bundle to a vector bundle over the real projective space |
| topic | Representation Theory Differential Geometry 22E46, 17B10 |
| url | https://arxiv.org/abs/2312.15621 |