#### Bulg. J. Phys. vol.33 no.s2 (2006), pp. 42-53

#### Calculation of Bethe Vectors in the **sl**_{N+1} Gaudin Model

**sl**

I. Scherbak

go back^{}*School of Mathematical Sciences of the Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel*Abstract.We deal with the Gaudin model associated with the tensor product ofhighest weightnsl_{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 casen=is basic, because the construction of iterated singular vectors allows to produce Bethe vectors in the tensor product of2>nrepresentations from the Bethe vectors in a certain sequence of basic cases. In the paper, we find Bethe vectors explicitly in the2specialbasic 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.)