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A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to An-type root system in both the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a Selberg-type integral and generalise it to the deformed An,1-case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integrals

Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra $\Xmathfrak {t}_{\hspace *{.3pt}n}$. We show that Gaudin subalgebras form a variety isomorphic to the moduli space $\bar M_{0,n+1}$ of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of $\bar M_{0,n+1}$ in a Grassmannian of (n−1)-planes in an n(n−1)/2-dimensional space. We show that the sheaf of Gaudin subalgebras over $\bar M_{0,n+1}$ is isomorphic to a sheaf of twisted first-order differential operators. For each representation of the Kohno-Drinfeld Lie algebra with fixed central character, we obtain a sheaf of commutative algebras whose spectrum is a coisotropic subscheme of a twisted version of the logarithmic cotangent bundle of $\bar M_{0,n+1}$

An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group SN is presented for integer values of the parameter. The corresponding integrals can be computed effectively as certain iterated residues determined by a given Young diagram and give polynomials with integer coefficients. The derivation is based on Schur-Weyl duality and the results of Matsuo on the original SU(n) KZ equation. The duality between the spaces of solutions with parameters m and −m is discussed in relation with the intersection pairing in the corresponding homology groups