Critical points of the product of powers of linear functions and families of bases of singular vectors
Solutions to the XXX type Bethe ansatz equations and flag varieties
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...
Conformal blocks in the tensor product of vector representations and localization formulas
Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.
Around the intersection form of an isolated singularity of hypersurface
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