Pieri-type formulas for the non-symmetric Jack polynomials

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dc.creatorForrester, P. J.
dc.creatorMcAnally, D. S.
dc.date2000-06-01
dc.date.accessioned2026-07-07T04:35:39Z
dc.date.available2026-07-07T04:35:39Z
dc.descriptionIn the theory of symmetric Jack polynomials the coefficients in the expansion of the $p$th elementary symmetric function $e_p(z)$ 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 $e_p(z) E_η(z)$ as a series in non-symmetric Jack polynomials are given. A known expansion formula for $z_i E_η(z)$ is rederived by an induction procedure, and this expansion is used to deduce the corresponding result for the expansion of $\prod_{j=1, j\ne i}^N z_j E_η(z)$, and consequently the expansion of $e_{N-1}(z) E_η(z)$. In the general $p$ case the coefficients for special terms in the expansion are presented.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0006006
dc.identifierhttp://arxiv.org/abs/math/0006006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59326
dc.subjectQuantum Algebra
dc.titlePieri-type formulas for the non-symmetric Jack polynomials
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