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

�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.

Accepté le :
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 
@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 = {https://www.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  - https://www.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 https://www.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. https://www.numdam.org/articles/10.4171/aihpd/19/
  • Dunkl, Charles F. Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points, Symmetry, Volume 13 (2021) no. 5, p. 779 | DOI:10.3390/sym13050779
  • González, Camilo; Lapointe, Luc The norm and the Evaluation of the Macdonald polynomials in superspace, European Journal of Combinatorics, Volume 83 (2020), p. 103018 | DOI:10.1016/j.ejc.2019.103018
  • Colmenarejo, Laura; Dunkl, Charles F.; Luque, Jean-Gabriel Factorizations of Symmetric Macdonald Polynomials, Symmetry, Volume 10 (2018) no. 11, p. 541 | DOI:10.3390/sym10110541

Cité par 3 documents. Sources : Crossref