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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 118, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.118 (Mi sigma1656) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2020.118
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.
Keywords: Jack polynomial, interpolation Jack polynomial, Pieri formula, kernel function.
Funding agency Grant number
Japan Society for the Promotion of Science 18J00233
This work was supported by Grant-in-Aid for JSPS Fellows (Number 18J00233).
Received: April 29, 2020; in final form November 14, 2020; Published online November 21, 2020
Bibliographic databases:
Document Type: Article
MSC: 05E05, 33C67, 43A90
Language: English
Citation: Genki Shibukawa, “New Pieri Type Formulas for Jack Polynomials and their Applications to Interpolation Jack Polynomials”, SIGMA, 16 (2020), 118, 11 pp.
Citation in format AMSBIB
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