| Project/Area Number |
26400004
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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 | Yamagata University |
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Principal Investigator |
Hayata Takahiro 山形大学, 大学院理工学研究科, 准教授 (50312757)
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| Research Collaborator |
ODA Takayuki 沖縄科学技術大学院大学, 教授 (10109415)
WATANABE Takao 大阪大学, 理学研究科, 教授 (30201198)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | エルミート定数 / 基本領域 / ジーゲル上半空間 / 最小ベクトル / キス数 / 球充填問題 / 格子 / シンプレクティック格子 / ランキン定数 / 完全行列 / シンプレクティック群 |
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| Outline of Final Research Achievements |
In this research, we propose an algorithm computing the kissing number of an element of classical groups and apply them to concrete cases. This algorithm uses the evaluation of determinants of the positive definite symmetric matrices in the Minkowski domain and so-called the short vector algorithm. The height of the linear transformation is by definition the modified ratio of the covolume of the transformed sublattice in the isotropic space and the covolume of the whole fixed lattice. The density is the minimum value of the height among modular transformation of the lattice and the kissing number is its cardinality modulo certain modular transformations. These are a generalization of the classical sphere packing problem. An application is when the symplectic group of degree 2, matrix size 4 and when the totally isotropic space is chosen. In this case, there
are three kinds of symplectic lattices who have locally maximal kissing numbers.
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