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

16 pages

References in corpus (2)

• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Coulomb integrals for the SL(2,R) WZNW model

Cited by in corpus (6)

• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• The sl_3 Selberg integral
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• Some recursive formulas for Selberg-type integrals
• Schur expansion of random-matrix reproducing kernels