Reseach on representations of association schemes

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400011
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Shinshu University
• Principal Investigator: HANAKI Akihide 信州大学, 学術研究院理学系, 教授 (50262647)
• Research Collaborator: YOSHIKAWA Masayoshi 兵庫教育大学, 学校教育研究科, 准教授 (10757743) ; SHIMABUKURO Osamu 長崎大学, 教育学部, 准教授 (40413736)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 代数学 / 組合せ論 / アソシエーション・スキーム / 表現 / 加群

Outline of Final Research Achievements

We studied on representations of association schemes and coherent configurations, especially modular representations. Their adjacency algebras are non semisimple, in general, and not studied so well. We computed some examples: half-cases, cyclotomic association schemes, and coherent configurations which correspond to symmetric designs. Also we studied [1] possibility of 6 dimensional non-commutative association schemes (with P.-H. Zieschang) [2] precise version of Clifford theorem for association schemes (with Y. Miyazaki) [3] block version of Maschke's theorem for association schemes.

Free Research Field

代数学