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Solutions to the XXX type Bethe ansatz equations and flag varieties

100%

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.

Bivariant Chern classes for morphisms with nonsingular target varieties

100%

Yokura S.

Open Mathematics

2005

tom 3

nr 4

614-626

W. Fulton and R. MacPherson posed the problem of unique existence of a bivariant Chern class-a Grothendieck transformation from the bivariant theory F of constructible functions to the bivariant homology theory H. J.-P. Brasselet proved the existence of a bivariant Chern class in the category of embeddable analytic varieties with cellular morphisms. In general however, the problem of uniqueness is still unresolved. In this paper we show that for morphisms having nonsingular target varieties there exists another bivariant theory $$\tilde {\mathbb{F}}$$ of constructible functions and a unique bivariant Chern class γ: $$\tilde {\mathbb{F}} \to {\mathbb{H}}$$ .

Ograniczanie wyników

2 Open Mathematics

1 Mukhin E.

1 Varchenko A.

1 Yokura S.

1 2005

1 2003

Wyniki wyszukiwania

Solutions to the XXX type Bethe ansatz equations and flag varieties

Bivariant Chern classes for morphisms with nonsingular target varieties