  The goal of the paper is to analyze a Gaudin model for a polynomial
representation of the Kohno-Drinfeld Lie algebra associated with the
multinomial distribution. The main result is the construction of an explicit
basis of the space of polynomials consisting of common eigenfunctions of Gaudin
operators in terms of Aomoto-Gelfand hypergeometric series. The construction
shows that the polynomials in this basis are also common eigenfunctions of the
operators for a dual Gaudin model acting on the degree indices, and therefore
they provide a solution to a multivariate discrete bispectral problem.
