2016 Fiscal Year Final Research Report
Explicit reduction theory of algebraic groups
| Project/Area Number |
26400012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HAYATA Takahiro 山形大学, 理工学研究科, 准教授 (50312757)
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| Research Collaborator |
Lee Tim Weng 大阪大学, 大学院理学研究科
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 基本領域 / 数論的部分群 / 簡約代数群 |
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| Outline of Final Research Achievements |
In this research project, we construct fundamental domains of arithmetic quotients of isotropic reductive groups over number fields by using Ryshkov domains. A Ryskov domain is defined by an arithmetical minimum function, which depends on a choice of a maximal parabolic subgroup. If we take different maximal parabolic subgroups, then we have different fundamental domains. In the case of general linear groups, we give explicit descriptions of several fundamental domains. Our construction gives a generalization of Korkine-Zorotareff reduction.
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| Free Research Field |
代数群の整数論
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