Clustering properties of rectangular Macdonald polynomials

  title={Clustering properties of rectangular Macdonald polynomials},
  author={Charles F. Dunkl and Jean-Gabriel Luque},
  journal={arXiv: Mathematical Physics},
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. 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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