Noncompact sl(N) Spin Chains: BGG-Resolution, Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices View Full Text


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Article Info

DATE

2011-08

AUTHORS

Sergey E. Derkachov, Alexander N. Manashov

ABSTRACT

We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite-dimensional auxiliary space are factorized into the product of N commuting Baxter -operators. We consider the transfer matrices with auxiliary spaces of a special type (including the finite-dimensional ones). It is shown that they can be represented as the alternating sum over the transfer matrices with infinite- dimensional auxiliary spaces. We show that certain combinations of the Baxter -operators can be identified with the Q-functions, which appear in the Nested Bethe Ansatz. More... »

PAGES

185-202

References to SciGraph publications

  • 1979-08. Quantum inverse problem method. I in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2003-10-23. Baxter ℚ-operator and separation of variables for the open SL(2,ℝ) spin chain in JOURNAL OF HIGH ENERGY PHYSICS
  • 1997-12. Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1996-04. Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1999-02. Integrable Structure of Conformal Field Theory III. The Yang–Baxter Relation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1997. Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations in LOW-DIMENSIONAL APPLICATIONS OF QUANTUM FIELD THEORY
  • 1981-09. Yang-Baxter equation and representation theory: I in LETTERS IN MATHEMATICAL PHYSICS
  • 1990-05. Chiral Potts model as a descendant of the six-vertex model in JOURNAL OF STATISTICAL PHYSICS
  • 2000-08. On Baxter's Q-Operator for the XXX Spin Chain in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1997-03. Quantum Lattice KdV Equation in LETTERS IN MATHEMATICAL PHYSICS
  • 2003-07-21. Separation of variables for the quantum SL(2,ℝ) spin chain in JOURNAL OF HIGH ENERGY PHYSICS
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    URI

    http://scigraph.springernature.com/pub.10.1007/s11005-011-0472-2

    DOI

    http://dx.doi.org/10.1007/s11005-011-0472-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1031293998


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