A comprehensive study of combinatorial objects by algebraic methods

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400034
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: TANAKA Hajime 東北大学, 情報科学研究科, 准教授 (50466546)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: アソシエーションスキーム / 距離正則グラフ / Terwilliger 代数 / 半正定値計画 / 直交多項式 / 符号 / 組合せデザイン

Outline of Final Research Achievements

I studied, from the viewpoints of both theory and applications, the representation theory of several non-commutative semisimple algebras, such as the Terwilliger algebra attached to each vertex of an association scheme, which is a certain special decomposition of a complete graph. I obtained various results related to extremal set theory, design theory, coding theory, etc., where the representation theory is applied together with the duality of semidefinite programming as well as systems of orthogonal polynomials associated with irreducible modules of these algebras. I have been involved with the recent development of the new tools, and this project contributed to further deepening and strengthening of them.

Free Research Field

代数的組合せ論