Abstract
The transfer matrix of the 6-vertex model of two-dimensional statistical physics commutes with many (more complicated) transfer matrices, but the latter, generally, do not commute with each other. The study of their action in the eigenspaces of the transfer matrix of the 6-vertex model becomes possible due to the “multiplicative property” of the vacuum curves of Λ-operators, from which the transfer matrices are constructed. This approach has allowed us, in particular, to discover for the first time the fact that the dimensions of the above-mentioned eigenspaces are multiples of (sufficiently large) degrees of the number 2. Bibliography: 14 titles.
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Dedicated to L. D. Faddeev on the occasion of his 60th birthday
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 215, 1994, pp. 163–177.
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Korepanov, I.G. Hidden symmetries in the 6-vertex model of statistical physics. J Math Sci 85, 1661–1670 (1997). https://doi.org/10.1007/BF02355327
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DOI: https://doi.org/10.1007/BF02355327