Research on characterizations of great antipodal sets as tight designs using representation theory

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K17604
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kitakyushu National College of Technology
• Principal Investigator: Kurihara Hirotake 北九州工業高等専門学校, 生産デザイン工学科, 准教授 (60637099)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 大対蹠集合 / 対称R空間 / デザイン

Outline of Final Research Achievements

Great antipodal sets on symmetric spaces are ``good'' finite subset of the spaces. In this research, we studied properties of Great antipodal sets on symmetric R-spaces in terms of combinatorics. In the area of combinatorics, we treat t-designs, which can approximate whole spaces.
In general, for a given a great antipodal set, it is not easy to determine t such that the set is a t-design. In this research, we obtained the relations between special irreducible representations and t such that the great antipodal set is a t-design. Moreover, we also obtained the fact that great antipodal sets have the structures of distance-transitive graphs.

Free Research Field

幾何学と組合せ論

Academic Significance and Societal Importance of the Research Achievements

対称空間の大対蹠集合を組合せ論の立場から研究することは我々の独自の視点であり、そのような研究を創出することは学術的な意義をもつと考える。大対蹠集合の組合せ論的情報から全体の空間の情報を引き出せることがわかったのは大変興味深く、対称空間の研究を組合せ論の言葉で翻訳できることは、今後の数学の発展にも寄与するものと考える。