Integral Representation of Solutions of the Elliptic Knizhnik–zamolodchikov–bernard Equations

@inproceedings{VARCHENKOIntegralRO,
title={Integral Representation of Solutions of the Elliptic Knizhnik–zamolodchikov–bernard Equations},
author={ALEXANDER VARCHENKO}
}

ALEXANDER VARCHENKO

We give an integral representation of solutions of the elliptic Knizhnik– Zamolodchikov–Bernard equations for arbitrary simple Lie algebras. If the level is a positive integer, we obtain formulas for conformal blocks of the WZW model on a torus. The asymptotics of our solutions at critical level gives eigenfunctions of Euler–Calogero–Moser integrable N-body systems. As a by-product, we obtain some remarkable integral identities involving classical theta functions.