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Solutions to the XXX type Bethe ansatz equations and flag varieties

E. Mukhin·A. Varchenko
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Abstract

We consider a version of the A_N Bethe equation of XXX type and introduce a reproduction 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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E. Mukhin, A. Varchenko. 2002-11-20. Solutions to the XXX type Bethe ansatz equations and flag varieties. https://arxiv.org/abs/math/0211321

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