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 the interpolation of Jack polynomials and intertwining relations for a kernel function for Jack polynomials.