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

  title={Integral Representation of Solutions of the Elliptic Knizhnik–zamolodchikov–bernard Equations},
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. 
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