Abstract.
It is known that for each matrix W i and it's transpose t W i in any four-weight spin model (X, W 1, W 2, W 3, W 4; D), there is attached the Bose-Mesner algebra of an association scheme, which we call Nomura algebra. They are denoted by N(W i ) and N(t W i ) = N′(W i ) respectively. H. Guo and T. Huang showed that some of them coincide with a self-dual Bose-Mesner algebra, that is, N(W 1) = N′(W 1) = N(W 3) = N′(W 3) holds. In this paper we show that all of them coincide, that is, N(W i ), N′(W i ), i=1, 2, 3, 4, are the same self-dual Bose-Mesner algebra.
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Received: June 17, 1999 Final version received: Januray 17, 2000
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Bannai, E. Bose-Mesner Algebras Associated with Four-Weight Spin Models. Graphs Comb 17, 589–598 (2001). https://doi.org/10.1007/PL00007251
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DOI: https://doi.org/10.1007/PL00007251