On a Selberg–Schur Integral

Abstract

A generalization of Selberg’s beta integral involving Schur polynomials associated with partitions with entries not greater than 2 is explicitly computed. The complex version of this integral is given after proving a general statement concerning the complex extensions of Selberg–Schur integrals. All these results have interesting applications in both mathematics and physics, particularly in conformal field theory, because the conformal blocks for the Wess–Zumino–Novikov–Witten model with underlying \({\widehat{\mathfrak{sl}}_2(\mathbb{R})_k}\) affine structure can be obtained by analytical continuation of these integrals.