Letters in Mathematical Physics

, Volume 106, Issue 3, pp 381–394 | Cite as

A Summation Formula for Macdonald Polynomials

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Abstract

We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases \({t = 1}\) and \({q = 0}\), we recover known expressions for the monomial symmetric and Hall–Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q–Whittaker polynomials.

Keywords

Macdonald polynomials 

Mathematics Subject Classification

Primary 05E05 33D80 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia

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