2000 Fiscal Year Final Research Report Summary
A collective study of algebraic combinatorics
| Project/Area Number |
09304004
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| Research Category |
Grant-in-Aid for Scientific Research (A).
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
BANNAI Eiichi Kyushu U.Facuety of Math, Professor, 大学院・数理学研究院, 教授 (10011652)
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| Co-Investigator(Kenkyū-buntansha) |
MUUEMOSA Akihiro Kyushu U.Facuety of Math, Assoc.Prof., 大学院・数理学研究院, 助教授 (50219862)
KOIKE Masao Kyushy U.Facuety of Math, Professor, 大学院・数理学研究院, 教授 (20022733)
BANNAI Etsuko Kyushu U.Facuety of Math, Assoc.Prof., 大学院・数理学研究院, 助教授 (00253394)
YAMAHI Hiroyoski Kumamoto Univ.Faclf.Scii.Professor, 理学部, 教授 (60028199)
SUZUKI Hiroshu International Chiaistian U.Professor, 教養学部, 教授 (10135767)
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| Project Period (FY) |
1997 – 2000
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| Keywords | Algebraic combinatorics / associationscheme / spin model / spherical design / modular form / code / finite ring / codes over finite alrelian group |
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| Research Abstract |
The main purpose of this grant was to support the overall developments of the research in algebraic combinatorics in Japan, by supporting the expenses of speakers and participants who attended the symposiums in this and related areas. Each year, we have about 2 large meetings and some smaller workshops. These large meetings were : the 14th (Mitaka, Tokyo), 15th (Kanazawa), 16th (Fukuoka) and 17 th (Tsukuba) Algebraic Combinatorics Symposiums ; and the conferences on algebraic combinatorics and/or related subjets which were held in RIMS annually for the last several years.
The current activities of algebraic combinatorics in Japan is very active and successful. We have had quite notable developments, in particular, on the subjects such as classification problems of association schemes and distance-regular graphs ; on spherical designs, on spin models, and on Terwilliger algebras and its connections with representation theory. One of the main research subjects in the close neighborhood of the principal investigator has been the study of codes over various finite rings and finite abelian groups, and then to apply these results to the studies of modular forms. We have obtained various results on self-dual codes and Type II codes over various rings. In addition, we have classified the finite index subgroups of SL (2, Z) whose ring of modular forms is isomorhpic to a polynomial ring. We have also started the study of modular forms of fractional weights, and then we found an interesting result (Bannai-Koike-Munemasa-Sekiguchi) on the modular forms of weghts 1/5-integers of Γ (5). We are currently continuing to work on further generalizations in this direction. The principal investigator has also started to work on the character tables of association schemes and trying to look at the object, by looking at them as a finite version of modular forms. Also, the principal investigator has started to study the modular data of finite groups as well as their modular invariants.
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