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Communications in Mathematical Physics

, Volume 256, Issue 3, pp 565–588 | Cite as

Discrete Miura Opers and Solutions of the Bethe Ansatz Equations

  • Evgeny Mukhin
  • Alexander Varchenko
Article

Abstract

Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra Open image in new window come in families called the populations. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra Open image in new window The proof is based on the correspondence between the solutions of the Bethe ansatz equations and special difference operators which we call the discrete Miura opers. The notion of a discrete Miura oper is one of the main results of the paper.

For a discrete Miura oper D, associated to a point of a population, we show that all solutions of the difference equation DY=0 are rational functions, and the solutions can be written explicitly in terms of points composing the population.

Keywords

Neural Network Statistical Physic Complex System Rational Function Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Evgeny Mukhin
    • 1
  • Alexander Varchenko
    • 2
  1. 1.Department of Mathematical SciencesIndiana University Purdue University IndianapolisIndianapolisUSA
  2. 2.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA

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