A D-module approach to invariant distributions with finitely many orbits
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911947758239744 |
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| author | Ochiai, Hiroyuki |
| author_facet | Ochiai, Hiroyuki |
| contents | Tauchi provides an example illustrating the action of a real algebraic subgroup $H$ of $GL(2n, \mathbb{R})$ with finitely many orbits on $\mathbb{R}^{2n}$, while the dimension of the space of relative $H$-invariant distributions on $\mathbb{R}^{2n}$ is infinite. We offer a perspective on this example from the viewpoint of D-modules, where we explicitly determine the simple quotient regular holonomic D-modules and demonstrate that the distributions exhibit an enlarged symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A D-module approach to invariant distributions with finitely many orbits Ochiai, Hiroyuki Representation Theory Tauchi provides an example illustrating the action of a real algebraic subgroup $H$ of $GL(2n, \mathbb{R})$ with finitely many orbits on $\mathbb{R}^{2n}$, while the dimension of the space of relative $H$-invariant distributions on $\mathbb{R}^{2n}$ is infinite. We offer a perspective on this example from the viewpoint of D-modules, where we explicitly determine the simple quotient regular holonomic D-modules and demonstrate that the distributions exhibit an enlarged symmetry. |
| title | A D-module approach to invariant distributions with finitely many orbits |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2402.17340 |