Geodesic
Clustering properties of rectangular Macdonald polynomials
Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 263-307

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�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 di�fference operators with signifi�cance 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.

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DOI : 10.4171/aihpd/19
Classification : 05-XX, 20-XX, 33-XX, 81-XX
Keywords: Fractional quantum Hall effect, clustering properties, Macdonald polynomials, Hecke algebras, multivariate polynomials 
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     author = {Dunkl, Charles  F. and Luque, Jean-Gabriel},
     title = {Clustering properties of rectangular {Macdonald} polynomials},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {263--307},
     volume = {2},
     number = {3},
     year = {2015},
     doi = {10.4171/aihpd/19},
     mrnumber = {3416837},
     zbl = {1322.05133},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/19/}
}
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Dunkl, Charles  F.; Luque, Jean-Gabriel. Clustering properties of rectangular Macdonald polynomials. Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 3, pp. 263-307. doi: 10.4171/aihpd/19

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