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Some comments on the solvable chiral Potts model. (English) Zbl 0715.14024

A proof of the conjecture of Baxter, Perk, Au-Yang on their new solution of the star-triangle equation is given. This conjecture is on the structure of some normalization factor R(p,q,r) of this model related with the general Fermat curve. Properties of the underlying curve \(x^ 3y^ 3+x^ 3+y^ 3+k^{-2}=0\) are established. The period matrix is calculated. The theta function is expressed in terms of the Jacobi theta functions. The Picard-Fuchs equations for the periods of holomorphic differentials are derived.
Reviewer: A.Bobenko

MSC:

14H42 Theta functions and curves; Schottky problem
32G20 Period matrices, variation of Hodge structure; degenerations
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
14K25 Theta functions and abelian varieties
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