Some recursive formulas for Selberg-type integrals

Abstract

A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previous results in Aomoto (1987) SIAM J. Math. Anal. 18 545–49 and Iguri (2009) Lett. Math. Phys. 89 141–58. These formulas provide a well-defined algorithm for computing Selberg–Schur integrals whenever the Kostka numbers relating Schur functions and the corresponding monomial polynomials are explicitly known. We illustrate the usefulness of our results discussing some interesting examples.