Clustering properties of rectangular Macdonald polynomials

2012/04/23 by Charles F. Dunkl, Dunkl, Charles F., Jean-Gabriel Luque +1
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math-ph #math.CO #math.MP #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1204.5117

43 pages, 2 figures

arxiv created 2013/02/24 · arxiv updated 2013/02/26

Abstract

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.

Related

• Factorizations of symmetric Macdonald polynomials
• Connections between vector-valued and highest weight Jack and Macdonald polynomials
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter α
• A combinatorial approach to the q,t-symmetry relation in Macdonald polynomials
• Factorization formulas for Macdonald polynomials