Abstract
We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. Consequently, we prove a conjecture of Bernevig and Haldane stated in the context of the fractional quantum Hall effect theory.
Highlights
Jack polynomials have many applications in physics, especially in statistical physics and quantum physics due to their relation to the many-body problem
Fractional quantum Hall (FQH) states of particles in the lowest Landau levels are described by such polynomials [1,2,3]
The problem is studied in the realm of Macdonald polynomials which form a (q, t)-deformation of the Jack polynomials related to the double affine Hecke algebra and the results are recovered by making degenerate the parameters q and t
Summary
Jack polynomials have many applications in physics, especially in statistical physics and quantum physics due to their relation to the many-body problem. The problem is studied in the realm of Macdonald polynomials which form a (q, t)-deformation of the Jack polynomials related to the double affine Hecke algebra and the results are recovered by making degenerate the parameters q and t. A very similar technique has been used in [5] to prove general formulas for perturbative correlators in basic matrix models that can be interpreted as the Schur-preservation property of Gaussian measures In this case, the substitution of Schur functions by Macdonald polynomials defines a deformation of the matrix model. Clustering properties are shown to be equivalent to very elegant formulas involving factorizations of Macdonald polynomials.
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