Uniform decomposition of the flag scheme by a symmetric subgroup action
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914965658533888 |
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| author | Hayashi, Takuma |
| author_facet | Hayashi, Takuma |
| contents | In this paper, we establish a scheme-theoretic analog of the works of Matsuki and Richardson--Springer on the symmetric subgroup orbit decomposition of the flag variety under a certain assumption that asserts local constancy of their combinatorial description of the classification of orbits at geometric points (the local constancy hypothesis). We also prove that scheme-theoretic models of orbits are affinely imbedded into the flag scheme under the same assumption (Beilinson--Bernstein's affinity theorem). Finally, we compute some classical examples to give scheme-theoretic consequences of the geometric point free and descent phenomena of orbit decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform decomposition of the flag scheme by a symmetric subgroup action Hayashi, Takuma Algebraic Geometry Representation Theory In this paper, we establish a scheme-theoretic analog of the works of Matsuki and Richardson--Springer on the symmetric subgroup orbit decomposition of the flag variety under a certain assumption that asserts local constancy of their combinatorial description of the classification of orbits at geometric points (the local constancy hypothesis). We also prove that scheme-theoretic models of orbits are affinely imbedded into the flag scheme under the same assumption (Beilinson--Bernstein's affinity theorem). Finally, we compute some classical examples to give scheme-theoretic consequences of the geometric point free and descent phenomena of orbit decompositions. |
| title | Uniform decomposition of the flag scheme by a symmetric subgroup action |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2410.04119 |