In the theory of symmetric Jack polynomials the coefficients in the expansion of the th elementary symmetric function 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 are explored. Necessary conditions for non-zero coefficients in the expansion of as a series in non-symmetric Jack polynomials are given. A known expansion formula for is rederived by an induction procedure, and this expansion is used to deduce the corresponding result for the expansion of , and consequently the expansion of . In the general case the coefficients for special terms in the expansion are presented.
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P. J. Forrester, D. S. McAnally, Pieri-type formulas for the non-symmetric Jack polynomials. Comment. Math. Helv. 79 (2004), no. 1, pp. 1–24DOI 10.1007/S00014-003-0789-2