2011 Fiscal Year Final Research Report
Various aspects of hyperplane arrangements
| Project/Area Number |
21340001
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University |
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Principal Investigator |
TERAO Hiroaki 北海道大学, 大学院・理学研究院, 教授 (90119058)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 代数的組合せ論 / 超平面配置 |
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| Research Abstract |
The definition of hyperplane arrangements is, like groups and rings, deceptively simple but they are not simplistic objects. In the first year of this research project, we successfully constructed a research network encompassing specialties and generations in order to understand diversified viewpoints of hyperplane arrangements in a wide spectrum and to hold a commanding position for advancing the research. Consequently, we studied the subject from various viewpoints including combinatorics, algebraic geometry, group theory, Lie algebra theory and statistics and described their mutual relations. The most conspicuous example is the relationship between the Weyl arrangements and the Bernoulli polynomials, which was discovered by us in 2010. It has been scrutinized and expected to develop further.
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