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 Uspekhi Mat. Nauk, 2003, Volume 58, Issue 3(351), Pages 51–88 (Mi umn628)

Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles

I. M. Kricheverabc, S. P. Novikovbd

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Columbia University
d University of Maryland

Abstract: Higher-rank solutions of the equations of the two-dimensionalized Toda lattice are constructed. The construction of these solutions is based on the theory of commuting difference operators, which is developed in the first part of the paper. It is shown that the problem of recovering the coefficients of commuting operators can be effectively solved by means of the equations of the discrete dynamics of the Tyurin parameters characterizing the stable holomorphic vector bundles over an algebraic curve.

DOI: https://doi.org/10.4213/rm628

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English version:
Russian Mathematical Surveys, 2003, 58:3, 473–510

Bibliographic databases:

Document Type: Article
UDC: 517.9
MSC: Primary 37K10, 47B39; Secondary 14H70, 37K20, 14H52, 14C40, 37K40, 35Q53, 81R12

Citation: I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Uspekhi Mat. Nauk, 58:3(351) (2003), 51–88; Russian Math. Surveys, 58:3 (2003), 473–510

Citation in format AMSBIB
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• https://doi.org/10.4213/rm628
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