Holomorphic Laplacian on the Lie ball and the Penrose transform
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909064288534528 |
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| author | Sekiguchi, Hideko |
| author_facet | Sekiguchi, Hideko |
| contents | We prove that any holomorphic function $f$ on the Lie ball of even dimension satisfying $Δf=0$ is obtained uniquely by the higher-dimensional Penrose transform of a Dolbeault cohomology for a twisted line bundle of a certain domain of the Grassmannian of isotropic subspaces. To overcome the difficulties arising from that the line bundle parameter is outside the {\it{good range}}, we use some techniques from algebraic representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic Laplacian on the Lie ball and the Penrose transform Sekiguchi, Hideko Representation Theory 22E46 (Primary) 43A85, 33C70, 32L25 (Secondary) We prove that any holomorphic function $f$ on the Lie ball of even dimension satisfying $Δf=0$ is obtained uniquely by the higher-dimensional Penrose transform of a Dolbeault cohomology for a twisted line bundle of a certain domain of the Grassmannian of isotropic subspaces. To overcome the difficulties arising from that the line bundle parameter is outside the {\it{good range}}, we use some techniques from algebraic representation theory. |
| title | Holomorphic Laplacian on the Lie ball and the Penrose transform |
| topic | Representation Theory 22E46 (Primary) 43A85, 33C70, 32L25 (Secondary) |
| url | https://arxiv.org/abs/2401.03432 |