New Pieri Type Formulas for Jack Polynomials and their Applications to Interpolation Jack Polynomials

Abstract

We present new Pieri type formulas for Jack polynomials. As an application, we give a new derivation of higher order difference equations for interpolation Jack polynomials originally found by Knop and Sahi. We also propose Pieri formulas for interpolation Jack polynomials and intertwining relations for a kernel function for Jack polynomials.