New Elliptic Solutions of the Yang–Baxter Equation View Full Text


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Article Info

DATE

2016-07

AUTHORS

D. Chicherin, S. E. Derkachov, V. P. Spiridonov

ABSTRACT

We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang–Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard Baxter’s R-matrix for the 8-vertex model and Sklyanin’s L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang–Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is also derived using the fusion formalism. More... »

PAGES

507-543

References to SciGraph publications

  • 2011-06. Elliptic Hypergeometry of Supersymmetric Dualities in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1982-10. Some algebraic structures connected with the Yang—Baxter equation in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 1982. Quantum spectral transform method recent developments in INTEGRABLE QUANTUM FIELD THEORIES
  • 1983-10. Some algebraic structures connected with the Yang—Baxter equation. Representations of quantum algebras in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 2005-06. The Vertex-Face Correspondence and the Elliptic 6j-Symbols in LETTERS IN MATHEMATICAL PHYSICS
  • 1997-08. Ruijsenaars' Commuting Difference Operators as Commuting Transfer Matrices in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1986-10. Fusion of the eight vertex SOS model in LETTERS IN MATHEMATICAL PHYSICS
  • 2007-06. An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic) in THE RAMANUJAN JOURNAL
  • 1981-09. Yang-Baxter equation and representation theory: I in LETTERS IN MATHEMATICAL PHYSICS
  • 1981-04. Baxter's equations and algebraic geometry in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 2001. Elliptic Beta Integrals and Special Functions of Hypergeometric Type in INTEGRABLE STRUCTURES OF EXACTLY SOLVABLE TWO-DIMENSIONAL MODELS OF QUANTUM FIELD THEORY
  • 2006-12. Fusion of Baxter’s Elliptic R-Matrix and the Vertex-Face Correspondence in ANNALES HENRI POINCARÉ
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-016-2590-2

    DOI

    http://dx.doi.org/10.1007/s00220-016-2590-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1050958040


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