Study on Ideal Subsrragenemnts of Weyl arrangements

2015 Fiscal Year Final Research Report

• Project/Area Number: 26610001
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: TERAO Hiroaki 北海道大学, 国際本部, 特任教授 (90119058)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 超平面配置 / ルート系 / ワイル配置 / 自由配置 / イデアル / 指数 / 高さ / 双対分割定理

Outline of Final Research Achievements

The main purpose of this research was to obtain new results, by applying the theory of hyperplane arrangements to the algebraic/geometric study of root systems or reflection groups in general, with a new depth which would not be reachable by the known approaches. The research began with explicit calculations with the intention to prove the first conjecture by Summers-Tymoczko in mind. Finally, we verified the dual partition theorem by Shapiro-Steinberg-Kostant-Macdonald, which is a celebrated theorem found in textbooks, for some restriction arrangements of the Weyl arrangements.

Free Research Field

数物系科学（数学・代数学）