Clustering properties of rectangular Macdonald polynomials

Details Clustering properties of rectangular Macdonald polynomials Clustering properties of rectangular Macdonald polynomials

2012-04-23

arxiv.org/abs/1204.5117v1

Physics

Mathematical Physics

25 pages, 2 figures

Scientific paper

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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