Uniform decomposition of the flag scheme by a symmetric subgroup action

Fuente: arXiv
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Auteur principal: Hayashi, Takuma
Format: Preprint
Publié: 2024
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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