Abstract.

We deal with the Gaudin model associated with the tensor product of n highest weight sl_N+1-representations. The Bethe Ansatz method reduces the problem of calculation common singular eigenvectors of the Gaudin Hamiltonians to the problem of solving a system of algebraic Bethe equations. The case n=2 is basic, because the construction of iterated singular vectors allows to produce Bethe vectors in the tensor product of n > 2 representations from the Bethe vectors in a certain sequence of basic cases. In the paper, we find Bethe vectors explicitly in the special basic case, i.e. when in addition one of the two highest weights is a multiple of the first fundamental weight. Our method is based on relations to the intersection theory in the Grassmannian of (N+1)-dimensional subspaces in the vector space of complex polynomials.

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