Association schemes and characters of finite groups
| Project/Area Number |
10640007
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tokyo Medical and Dental University |
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Principal Investigator |
KIYOTA Masao College of Liberal Arts and Sciences, Tokyo Medical and Dental University, Professor, 教養部, 教授 (50214911)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| 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)
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| Keywords | association scheme / finite group / Cartan matrix / sharp character |
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| 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 Q-polynomial. 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 distance-regular 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 p-solvable groups, we had the complete determination of their Cartan matrices. (T. Wada)
5. In p-solvable 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, p-good groups and good modules. We had conjectures on the structures of p-good groups and good modules, and we studied (are now studying) them. (M. Kiyota)
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Report
(3 results)
Research Products
(20 results)
