2000/06/01 by Peter J. Forrester, P. J. Forrester, Forrester, P. J. +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0006006
19 pages
arxiv created 2000/06/01 · openalex publication_date 2000/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the theory of symmetric Jack polynomials the coefficients in the expansion of the pth elementary symmetric function ep(z) times a Jack polynomial expressed as a series in Jack polynomials are known explicitly. Here analogues of this result for the non-symmetric Jack polynomials Eη(z) are explored. Necessary conditions for non-zero coefficients in the expansion of ep(z) Eη(z) as a series in non-symmetric Jack polynomials are given. A known expansion formula for zi Eη(z) is rederived by an induction procedure, and this expansion is used to deduce the corresponding result for the expansion of ∏j=1, j≠ iN zj Eη(z), and consequently the expansion of eN-1(z) Eη(z). In the general p case the coefficients for special terms in the expansion are presented.