Some recursive formulas for Selberg-type integrals

TL;DR

This paper derives recursive formulas for Selberg-type integrals involving monomial symmetric polynomials, enabling efficient computation of Selberg-Schur integrals through known Kostka numbers, and demonstrates their practical utility with examples.

Contribution

The paper introduces new recursive relations for Selberg-type integrals that generalize previous results and facilitate their computation using Kostka numbers.

Findings

Recursive formulas for Selberg-type integrals are established.

The formulas enable algorithmic computation of Selberg-Schur integrals.

Examples demonstrate the effectiveness of the derived relations.

Abstract

A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. 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.