Abstract
As a generalization of symmetric spin models, a four-weight spin model (X; W1, W2, W3, W4) consists of a finite set X and four non-zero complex matrices indexed by elements of X satisfying certain conditions set for polynomial invariants of links and knots in R3 through their partition functions. We show that W4tW4 = tW4W4, W1°tW1 lie in a certain symmetric Bose-Mesner algebra using spectral techniques. Based on this algebra, we then show that entries of W1 were essentially determined by its subconstituent algebra.
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