Pieri-type formulas for the non-symmetric Jack polynomials

Abstract

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 E η(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 ziEη(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 coeffi..