Project/Area Number  10640007 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Algebra

Research Institution  Tokyo Medical and Dental University 
Principal Investigator 
KIYOTA Masao College of Liberal Arts and Sciences, Tokyo Medical and Dental University, Professor, 教養部, 教授 (50214911)

CoInvestigator(Kenkyūbuntansha) 
WADA Tomoyuki Tokyo University of Agriculture and Technology, Department of Mathematics, Professor, 工学部, 教授 (30134795)
NOMURA Kazumasa College of Liberal Arts and Sciences, Tokyo Medical and Dental University, Professor, 教養部, 教授 (40111645)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1999 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1998 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  association scheme / finite group / Cartan matrix / sharp character / アソシエーションスキーム / 有限群 / カルタン行列 / シャープ指標 
Research Abstract 
We obtained the following results on our research project. 1. We had the complete classification of finite groups whose group association schemes are Qpolynomial. We note that all these groups have sharp characters. (M. Kiyota and H. Suzuki) 2. We obtained a general formulas (with two parameters) for spin models on distanceregular graphs (K. Nomura) 3. We obtained a relation between the number of characters in a block and the Cartan integers. Using the relation, we get the lower bound of the maximal eigenvalue of the Cartan matrix. (T. Wada) 4. For a certain family of psolvable groups, we had the complete determination of their Cartan matrices. (T. Wada) 5. In psolvable groups, we obtained the condition under which the eigenvalues and the elementary divisors of Cartan matrix are coincide. (M. Kiyota and T. Wada) 6. We had a new concepts, pgood groups and good modules. We had conjectures on the structures of pgood groups and good modules, and we studied (are now studying) them. (M. Kiyota)
