Raising type twisted Pieri formulas for Jack polynomials and their applications to interpolation Jack polynomials
Genki Shibukawa
TL;DR
This paper introduces new Pieri formulas for Jack polynomials, providing alternative proofs for interpolation Jack polynomial formulas and extending twisted Pieri formulas to binomial type polynomials like Jack and Bernoulli polynomials.
Contribution
It presents novel Pieri formulas for Jack polynomials, offering new proofs and generalizations to broader classes of polynomials.
Findings
New Pieri formulas for Jack polynomials
Alternative proof of interpolation Jack polynomial formulas
Extension of twisted Pieri formulas to binomial type polynomials
Abstract
We propose new Pieri type formulas for Jack polynomials, which is another kind of Pieri type formulas than the ones in the previous paper (G. Shibukawa, arXiv:2004.12875). From these new Pieri type formulas, we give yet another proof of difference and Pieri formulas for interpolation Jack polynomials. Further, we also generalize a falling type twisted Pieri formula to the binomial type polynomials including Jack and multivariate Bernoulli polynomials.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Nonlinear Waves and Solitons