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This article is cited in 30 scientific papers (total in 30 papers)
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.
Received: 15.04.2003
Citation:
I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510
Linking options:
https://www.mathnet.ru/eng/rm628https://doi.org/10.1070/RM2003v058n03ABEH000628 https://www.mathnet.ru/eng/rm/v58/i3/p51
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