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Solutions to the XXX type Bethe ansatz equations and flag varieties

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Mukhin E., Varchenko A.

Open Mathematics

2003

tom 1

nr 2

238-271

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.

Ograniczanie wyników

1 Open Mathematics

1 Mukhin E.

1 Varchenko A.

1 2003

Wyniki wyszukiwania

Solutions to the XXX type Bethe ansatz equations and flag varieties