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Solutions to the XXX type Bethe ansatz equations and flag varieties

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Central European Journal of Mathematics

Abstract

We consider a version of the A N 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 sl N +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 B N and C N . Populations of B N and C N type are isomorphic to the flag varieties of C N and B N types respectively.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 North Blackford St, 46202-3216, Indianapolis, IN, USA

    E. Mukhin

  2. Department of Mathematics, University of North Carolina at Chapel Hill, 27599-3250, Chapel Hill, NC, USA

    A. Varchenko

Authors
  1. E. Mukhin
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  2. A. Varchenko
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Mukhin, E., Varchenko, A. Solutions to the XXX type Bethe ansatz equations and flag varieties. centr.eur.j.math. 1, 238–271 (2003). https://doi.org/10.2478/BF02476011

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  • DOI: https://doi.org/10.2478/BF02476011

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