Solutions to the XXX type Bethe ansatz equations and flag varieties
- Cite this article as:
- Mukhin, E. & Varchenko, A. centr.eur.j.math. (2003) 1: 238. doi:10.2478/BF02476011
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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.