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Russian Mathematical Surveys, 2003, Volume 58, Issue 3, Pages 473–510
DOI: https://doi.org/10.1070/RM2003v058n03ABEH000628 (Mi rm628) 		 
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
English version PDF (368 kB) Citations (30)
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DOI: https://doi.org/10.1070/RM2003v058n03ABEH000628
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
Russian version:
Uspekhi Matematicheskikh Nauk, 2003, Volume 58, Issue 3(351), Pages 51–88
DOI: https://doi.org/10.4213/rm628
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 37K10, 47B39; Secondary 14H70, 37K20, 14H52, 14C40, 37K40, 35Q53, 81R12
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 30 articles:
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