2003 Fiscal Year Final Research Report Summary
Structures and Representations of Association Schemes
| Project/Area Number |
12640039
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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 | College of Liberal Arts, International Christian University |
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Principal Investigator |
SUZUKI Hiroshi International Christian University, College of Liberal Arts, Professor, 教養学部・理学科, 教授 (10135767)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMIZU Yuji International University, Associate Professor, 教養学部, 準教授 (80187468)
HORAI Masako International Christian University, Professor, 教養学部, 教授 (00015588)
MORIMOTO Mitsuo International Christian University, College of Liberal Arts, Professor, 教養学部, 教授 (80053677)
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| Project Period (FY) |
2000 – 2003
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| Keywords | association schemes / representations of finite groups / characters of finite groups / distance-regular graphs / spin models / algebraic combinatorics |
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| Research Abstract |
a. Connection between Algebra and Geometry: The Terwilliger algebra with respect to a base subset of a distance-regular grasph was defined and studied extensively. The use of this algebra enables to investigate modules of Terwilliger algebras of any endpoint much easily and gives a connection between the theory of Delsarte and Terwilliger algebra and its modules.
b. Balanced Conditions: Q-polynomial group association schemes were classified.
c. Weakly Distance-Regular Digraphs: The definition of weakly distance-regular digraphs together with various constructions were given. Partly as a joint work with Kaishun Wang, classifications of the case with degree 2, and regular group cases, which are called thin, were completed. Degree 3 cases and girth 2 cases are inprogress.
d. Type II Matrices: As a joint work with Rie Hosoya, it was shown that if a type II matrix is imprimitive, it can be decomposed as a generalized tensor product of type II matrices of smaller size. The application of this result to a classification of imprimitive spin models is expected.
e. Absolute Bound Conjecture of Distance-Regular Graphs and Related Topics: A classification of distance-regular graphs of order (s, 2) was completed and published. The use of Terwilliger algebra was proved to be useful. In particular, if the graph is 3-thin, geometric girths are bounded by 11.
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