1998 Fiscal Year Final Research Report Summary
Spin models and modular invariance
| Project/Area Number |
09640013
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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 |
NOMURA Kazumasa Tokyo Medical and Dental University Professor, 教養部, 教授 (40111645)
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| Co-Investigator(Kenkyū-buntansha) |
KIYOTA Masao Tokyo Medical and Dental University Professor, 教養部, 教授 (50214911)
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| Project Period (FY) |
1997 – 1998
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| Keywords | spin model / association scheme / modular invariance / Bose-Mesner algebra |
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| Research Abstract |
We obtained the following results about spin models and Bose-Mesner algebras.
(1) We constructed a Bose-Mesner algebra N(W) containing W for any symmetric spin model 147 (by K.Nomura).
(2) We generalized N(W) in case of non-symmetric spin model W.Moreover, we have shown that N(W) is self-dual and it satisfies modular invariance property (by K.Nomura, F.Jaeger, M.Matsumoto).
(3) We obtained a structure theorem for non-symmetric spin models, and we introduced the notion of "index of a spin model" (by K.Nomura, F.Jaeger). Using this result, we now classifying non-symmetric spin models (with T.Ikuta).
(4) We obtained a general formulas for spin models on distance-regular graphs (by K.Nomura, B.curtin). Acturally if N(W) is P-polynomial, then N(W) is described by only two parameters.
(5) We completely classified type II matrices of size 5 (by K.Nomura).
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Research Products
(12 results)
