Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 16 (2020), 118, 11 pages      arXiv:2004.12875      https://doi.org/10.3842/SIGMA.2020.118
Contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum Field Theory

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

Genki Shibukawa
Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Received April 29, 2020, in final form November 14, 2020; Published online November 21, 2020

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.

Key words: Jack polynomial; interpolation Jack polynomial; Pieri formula; kernel function.

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