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Uspekhi Mat. Nauk, 1995, Volume 50, Issue 6(306), Pages 3–56 (Mi umn1121)  

This article is cited in 47 scientific papers (total in 47 papers)

Spin generalization of the Ruijsenaars–Schneider model, the non-Abelian Toda chain, and representations of the Sklyanin algebra

I. M. Krichevera, A. V. Zabrodinb

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Institute of biochemical physics of the Russian Academy of Sciences

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English version:
Russian Mathematical Surveys, 1995, 50:6, 1101–1150

Bibliographic databases:

UDC: 512
MSC: 20E05, 35Q53
Received: 29.05.1995

Citation: I. M. Krichever, A. V. Zabrodin, “Spin generalization of the Ruijsenaars–Schneider model, the non-Abelian Toda chain, and representations of the Sklyanin algebra”, Uspekhi Mat. Nauk, 50:6(306) (1995), 3–56; Russian Math. Surveys, 50:6 (1995), 1101–1150

Citation in format AMSBIB
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\by I.~M.~Krichever, A.~V.~Zabrodin
\paper Spin generalization of the Ruijsenaars--Schneider model, the non-Abelian Toda chain, and representations of the Sklyanin algebra
\jour Uspekhi Mat. Nauk
\yr 1995
\vol 50
\issue 6(306)
\pages 3--56
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\transl
\jour Russian Math. Surveys
\yr 1995
\vol 50
\issue 6
\pages 1101--1150
\crossref{https://doi.org/10.1070/RM1995v050n06ABEH002632}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chalykh O., Fairon M., “On the Hamiltonian Formulation of the Trigonometric Spin Ruijsenaars-Schneider System”, Lett. Math. Phys.  crossref  isi
    2. Fairon M., Feher L., Marshall I., “Trigonometric Real Form of the Spin Rs Model of Krichever and Zabrodin”, Ann. Henri Poincare  crossref  isi
    3. G. E. Arutyunov, L. O. Chekhov, S. A. Frolov, “ R-Matrix quantization of the elliptic Ruijsenaars-Schneider model”, Theor Math Phys, 111:2 (1997), 536  mathnet  crossref  mathscinet  zmath  isi  elib
    4. S.N.M. Ruijsenaars, “Integrable Particle Systems vs Solutions to the KP and 2D Toda Equations”, Annals of Physics, 256:2 (1997), 226  crossref
    5. A. V. Zabrodin, “Hirota equation and Bethe ansatz”, Theor Math Phys, 116:1 (1998), 782  mathnet  crossref  mathscinet  zmath  isi  elib
    6. S N M Ruijsenaars, J Phys A Math Gen, 32:9 (1999), 1737  crossref  mathscinet  zmath  adsnasa  isi
    7. S. N. M. Ruijsenaars, “Generalized Lamé functions. I. The elliptic case”, J Math Phys (N Y ), 40:3 (1999), 1595  crossref  mathscinet  zmath  adsnasa  isi
    8. H.W. Braden, A. Marshakov, A. Mironov, A. Morozov, “The Ruijsenaars-Schneider model in the context of Seiberg-Witten theory”, Nuclear Physics B, 558:1-2 (1999), 371  crossref
    9. Ruijsenaars, SNM, “Hilbert space theory for reflectionless relativistic potentials”, Publications of the Research Institute For Mathematical Sciences, 36:6 (2000), 707  crossref  mathscinet  zmath  isi
    10. A. Marshakov, “Duality in integrable systems and generating functions for new Hamiltonians”, Physics Letters B, 476:3-4 (2000), 420  crossref
    11. S N M Ruijsenaars, J Phys A Math Gen, 34:48 (2001), 10595  crossref  mathscinet  zmath  adsnasa  isi
    12. S N M Ruijsenaars, “Reflectionless Analytic Difference Operators II. Relations to Soliton Systems”, Journal of Nonlinear Mathematical Physics, 8:2 (2001), 256  crossref
    13. D. V. Talalaev, “The Elliptic Gaudin System with Spin”, Theoret. and Math. Phys., 130:3 (2002), 361–374  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. A. V. Odesskii, V. N. Rubtsov, “Polynomial Poisson Algebras with Regular Structure of Symplectic Leaves”, Theoret. and Math. Phys., 133:1 (2002), 1321–1337  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “Elliptic Families of Solutions of the Kadomtsev–Petviashvili Equation and the Field Elliptic Calogero–Moser System”, Funct. Anal. Appl., 36:4 (2002), 253–266  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. A. V. Odesskii, “Elliptic algebras”, Russian Math. Surveys, 57:6 (2002), 1127–1162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. H.W. Braden, A. Gorsky, A. Odesskii, V. Rubtsov, “Double-elliptic dynamical systems from generalized Mukai–Sklyanin algebras”, Nuclear Physics B, 633:3 (2002), 414  crossref
    18. Chalykh, O, “Generalized Lame operators”, Communications in Mathematical Physics, 239:1–2 (2003), 115  crossref  mathscinet  zmath  adsnasa  isi
    19. Treibich, A, “Difference analogs of elliptic KdV solitons and Schrodinger operators”, International Mathematics Research Notices, 2003, no. 6, 313  crossref  mathscinet  zmath  isi
    20. Luen-Chau Li, “Poisson Involutions, Spin Calogero–Moser Systems Associated with Symmetric Lie Subalgebras and the Symmetric Space Spin Ruijsenaars-Schneider Models”, Comm Math Phys, 265:2 (2006), 333  crossref  mathscinet  zmath  adsnasa  isi
    21. V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    22. Oleg Chalykh, “Bethe Ansatz for the Ruijsenaars Model of $BC_1$-Type”, SIGMA, 3 (2007), 028, 9 pp.  mathnet  crossref  mathscinet  zmath
    23. Plamen Iliev, “Rational Ruijsenaars–Schneider hierarchy and bispectral difference operators”, Physica D: Nonlinear Phenomena, 229:2 (2007), 184  crossref
    24. I. M. Krichever, “Abelian solutions of the soliton equations and Riemann–Schottky problems”, Russian Math. Surveys, 63:6 (2008), 1011–1022  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    25. Chalykh, O, “Algebro-geometric Schrodinger operators in many dimensions”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 947  crossref  mathscinet  zmath  adsnasa  isi
    26. F. L. Soloviev, “On the Hamiltonian form of equations of the elliptic spin Ruijsenaars–Schneider model”, Russian Math. Surveys, 64:6 (2009), 1142–1144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    27. Igor Krichever, “Characterizing Jacobians via trisecants of the Kummer variety”, Ann of Math, 172:1 (2010), 485  crossref
    28. Krichever I., “Characterizing Jacobians via Trisecants of the Kummer Variety”, Ann. Math., 172:1 (2010), 485–516  isi
    29. Zabrodin A., “Intertwining operators for Sklyanin algebra and elliptic hypergeometric series”, J Geom Phys, 61:9 (2011), 1733–1754  crossref  isi
    30. A Levin, M Olshanetsky, A Smirnov, A Zotov, “Characteristic classes of $SL(N, {\mathbb {C}})$-bundles and quantum dynamical elliptic R-matrices”, J. Phys. A: Math. Theor, 46:3 (2013), 035201  crossref
    31. A. V. Zabrodin, “The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function”, Theoret. and Math. Phys., 174:1 (2013), 52–67  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    32. Eric Rains, Simon Ruijsenaars, “Difference Operators of Sklyanin and van Diejen Type”, Commun. Math. Phys, 2013  crossref
    33. Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., “Classical Tau-Function for Quantum Spin Chains”, J. High Energy Phys., 2013, no. 9, 064  crossref  isi
    34. Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.  mathnet  crossref  mathscinet
    35. A. Levin, M. Olshanetsky, A. Zotov, “Relativistic classical integrable tops and quantum R-matrices”, J. High Energ. Phys, 2014:7 (2014)  crossref
    36. G Aminov, S Arthamonov, A Smirnov, A Zotov, “Rational top and its classicalr-matrix”, J. Phys. A: Math. Theor, 47:30 (2014), 305207  crossref
    37. A. Levin, M. Olshanetsky, A. Zotov, “Classical integrable systems and soliton equations related to eleven-vertex R-matrix”, Nuclear Physics B, 2014  crossref
    38. A. Zabrodin, A. Zotov, “Classical-Quantum Correspondence and Functional Relations for Painlevé Equations”, Constr Approx, 2015  crossref
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    40. A. K. Pogrebkov, “Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions”, Theoret. and Math. Phys., 187:3 (2016), 823–834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    41. Mauleshova G.S. Mironov A.E., “One-Point Commuting Difference Operators of Rank One and Their Relation With Finite-Gap Schrodinger Operators”, Dokl. Math., 97:1 (2018), 62–64  crossref  isi
    42. A. V. Zabrodin, “Matrix modified Kadomtsev–Petviashvili hierarchy”, Theoret. and Math. Phys., 199:3 (2019), 771–783  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    43. A. V. Zotov, “Relativistic interacting integrable elliptic tops”, Theoret. and Math. Phys., 201:2 (2019), 1565–1580  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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