  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.
