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Annales de l’Institut Henri Poincaré D

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Volume 2, Issue 3, 2015, pp. 263–307
DOI: 10.4171/AIHPD/19

Published online: 2015-08-28

Clustering properties of rectangular Macdonald polynomials

Charles F. Dunkl[1] and Jean-Gabriel Luque[2]

(1) University of Virginia, Charlottesville, USA
(2) Université de Rouen, Saint-Étienne-du-Rouvray, France

The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials (which are also the quantum eigenfunctions of a familly of commuting difference operators with significance in the relativistic Ruijsenaars–Schneider model). The present paper is devoted to the proof of this formula. To this aim we use four families of Jack/Macdonald polynomials: symmetric homogeneous, nonsymmetric homogeneous, shifted symmetric and shifted nonsymmetric.

Keywords: Fractional quantum Hall effect, clustering properties, Macdonald polynomials, Hecke algebras, multivariate polynomials

Dunkl Charles , Luque Jean-Gabriel: Clustering properties of rectangular Macdonald polynomials. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 2 (2015), 263-307. doi: 10.4171/AIHPD/19