Central European Journal of Mathematics

, Volume 1, Issue 2, pp 238–271

Solutions to the XXX type Bethe ansatz equations and flag varieties

  • E. Mukhin
  • A. Varchenko

DOI: 10.2478/BF02476011

Cite this article as:
Mukhin, E. & Varchenko, A. centr.eur.j.math. (2003) 1: 238. doi:10.2478/BF02476011


We consider a version of the AN Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the slN+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems BN and CN. Populations of BN and CN type are isomorphic to the flag varieties of CN and BN types respectively.


algebraic Bethe anzatz Schubert Calculus descrete Wronskian 

MSC (2000)

82B23 14C17 17B37 

Copyright information

© Central European Science Journals 2003

Authors and Affiliations

  • E. Mukhin
    • 1
  • A. 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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