| Project/Area Number |
15K13430
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nara National College of Technology |
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Principal Investigator |
Nagura Makoto 奈良工業高等専門学校, 一般教科, 准教授 (30375399)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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)
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| Keywords | クイバーに付随する表現 / 正則概均質ベクトル空間 / スターリング数 / 重み付きグラフ / 代数学 / 概均質ベクトル空間 |
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| Outline of Final Research Achievements |
We obtained the number of standard forms of the bases of lattices that are spanned by subsets of irreducible and reduced root systems. In this result is expressed by a unified (and generalized) Stirling numbers. In particular, our result gives an combinatorial example of inversion formula for unified Stirling numbers.
In general, the ground field of prehomogeneous vector spaces associated with valued graphs may not be algebraically closed. We studied, in particular, such prehomogeneous vector spaces under the assumption that they are regular; and then we counted the number of them.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の成果により，クイバーに付随する表現を格子の観点から調べる際に必要な計算のための手がかり（すなわち，例えば格子の基底の標準形，正則概均質ベクトル空間を与える格子の個数など）が得られた．
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