2003 Fiscal Year Final Research Report Summary
Spin Models and Distance-Regular Graphs
| Project/Area Number |
14540010
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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, College of Liberal Arts and Sciences, Professor, 教養部, 教授 (40111645)
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| Co-Investigator(Kenkyū-buntansha) |
KIYOTA Masao Tokyo Medical and Dental University, College of Liberal Arts and Sciences, Professor, 教養部, 教授 (50214911)
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| Project Period (FY) |
2002 – 2003
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| Keywords | spin model / association scheme / Bose-Mesner algebra / distance-regular graph / 1-homogeneous / Terwilliger algebra |
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| Research Abstract |
Our purpose is to study properties of Bose-Mesner algebras which support spin models. We obtaind the following results:
(1) It was shown. that every Bose-Mesner algebra which supports a spin model 'should be strongly self-dual.
(2) We obtained some properties of real solutions of the modular invariance equation associated to spin models on distance-regular graphs.
(3) We characterized nonsymrnetric Hadamard models. This enables us to classify nonsymmetric spin models with small index.
(4) It was shown that every DRG supporting a spin model should be 1-homogeneous.
(5) We obtained an algebraic characterization of 1-homogeneous property.
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