On a Selberg-Schur integral

Understand

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, since the conformal blocks for the $SL(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten model can be obtained by analytical continuation of these integrals.