Duality Maps of Finite Abelian Groups and Their Applications to Spin Models

Journal of Algebraic Combinatorics

Volumn 8, Issue 3, 1998, Pages 223-233

  Bannai, Etsuko ^a   Munemasa, Akihiro ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

Association scheme; Finite abelian group; Quadratic form; Spin model

Indexed keywords

EID: 0040119935     PISSN: 09259899     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008613331395     Document Type: Article

References (13)

1. E. Bannai, "Modular invariance property and spin models attached to cyclic group association schemes," J. Statistical Planning and Inference 51 (1996), 107-124.
2. E. Bannai and E. Bannai, "Generalized spin models and association schemes," Memoirs Fac. Sci. Kyushu Univ. Ser. A 47 (1993), 397-409.
3. E. Bannai and E. Bannai, "Spin models on finite cyclic groups," J. Alg. Combin. 3 (1994), 243-259.
4. E. Bannai, E. Bannai, and F. Jaeger, "On spin models, modular invariance and duality," J. Alg. Combin. (to appear).
5. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Berlin-Heidelberg, 1989.
6. F. Jaeger, "Strongly regular graphs and spin models for the Kauffman polynomial," Geom. Ded. 44 (1992), 23-52.
7. F. Jaeger, "On spin models, triply regular association schemes, and duality," J. Alg. Combin. (to appear).
8. F. Jaeger, M. Matsumoto, and K. Nomura, "Association schemes related with type II matrices and spin models," J. Alg. Combin. 8 (1998), 39-72.
9. V.F.R. Jones, "On knot invariants related to some statistical mechanical models," Pac. J. Math. 137 (1989), 311-336.
10. V. Kac and M. Wakimoto, "A construction of generalized spin models," Proc. Conf. Math. Phys. (1994), 131-156.
11. Y. Kawada, "Über den Dualitätssatz der Charaktere nichtcommutativer Gruppen," Proc. Phys. Math. Soc. Japan, 24(3), (1942), 97-109.
12. K. Kawagoe, A. Munemasa, and Y. Watatani, "Generalized spin models," J. Knot Theory and Its Ramifications 3 (1994), 465-475.
13. Y. Kitaoka, Arithmetic of Quadratic Forms, Cambridge University Press, 1993.