�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 -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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Publié le :
DOI : 10.4171/aihpd/19
Publié le :
DOI : 10.4171/aihpd/19
Classification :
05-XX, 20-XX, 33-XX, 81-XX
Mots-clés : Fractional quantum Hall effect, clustering properties, Macdonald polynomials, Hecke algebras, multivariate polynomials
Mots-clés : Fractional quantum Hall effect, clustering properties, Macdonald polynomials, Hecke algebras, multivariate polynomials
@article{AIHPD_2015__2_3_263_0, 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://archive.numdam.org/articles/10.4171/aihpd/19/} }
TY - JOUR AU - Dunkl, Charles F. AU - Luque, Jean-Gabriel TI - Clustering properties of rectangular Macdonald polynomials JO - Annales de l’Institut Henri Poincaré D PY - 2015 SP - 263 EP - 307 VL - 2 IS - 3 UR - http://archive.numdam.org/articles/10.4171/aihpd/19/ DO - 10.4171/aihpd/19 LA - en ID - AIHPD_2015__2_3_263_0 ER -
%0 Journal Article %A Dunkl, Charles F. %A Luque, Jean-Gabriel %T Clustering properties of rectangular Macdonald polynomials %J Annales de l’Institut Henri Poincaré D %D 2015 %P 263-307 %V 2 %N 3 %U http://archive.numdam.org/articles/10.4171/aihpd/19/ %R 10.4171/aihpd/19 %G en %F AIHPD_2015__2_3_263_0
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. http://archive.numdam.org/articles/10.4171/aihpd/19/
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