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Additional info for Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 1
C. H. Sah, Prof. M. L. Yan and Prof. A. B. Zamolodchikov. Solvable Models and Riemann Surfaces 39 This work has been supported by the National Science Foundation under Grant DMR-8505419. References  H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M. L. Yan, Phys. Lett. 123A (1987) 219.  The case N = 4 is treated in B. M. McCoy, J. H. H. Perk, S. Tang, and C. H. Sah, Phys. Lett. 125 A (1987) 9.  R. J. Baxter, Phys. Rev. Lett. 26 (1971) 832; Ann. Phys. 70 (1972) 193.  See, for example, V.
Frameworks. More precisely, we will show that the diagram of Fig. M. T. frameworks; this will provide positive answers to our second and third questions for the case of two-particle and two-field states. In this diagram, sd will denote a relevant space of "test-functions" / with appropriate analyticity properties, and sA' a corresponding space of distribu- 54 J. Bros (sé = si/») ► sé' ^r-L2(R(%) FIGURE 1 tions or analytic functional Ψ (namely the "wave-functions") which will satisfy a certain Schrödinger-type equation σ · Ψ = 0.
This will surely lead to new solvable models. Similarly, the higher-genus Z N models should be studied in triangular lattices. This must almost surely lead to new solvable models. But these may very well not lead to any new Riemann surfaces. Instead, the situation may be like the genus-one case and will produce either the same free theory as the chiral Potts case or produce an interacting parafermion theory just as the eight-vertex model produces an interacting fourfermion theory. Indeed, the major unsolved conceptual problem at this stage is the following: can one expect to find a system of commuting transfer matrices for any Riemann surface, or are there special properties, such as a large group of automorphisms, which a Riemann surface must possess before it can produce a set of commuting transfer matrices?