Jack polynomial fractional quantum Hall states and their generalizations

Abstract

In the the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with $\alpha =-(r-1)/(k+1)$, $(r-1)$ and $(k+1)$ relatively prime, and with partition given in terms of its frequencies by $[n_0{0}^{(r-1)s}k{0}^{r-1}k{0}^{r-1}k\cdots 0^{r-1}m]$ satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.

arXiv comment19 pages, some typographical errors corrected and a reference added

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Cited by in corpus (9)

• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
• Vector-Valued Jack Polynomials from Scratch
• Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
• On the Structure of Edge State Inner Products in the Fractional Quantum Hall Effect
• Unified Fock space representation of fractional quantum Hall states
• Jack on a Devil's staircase
• Jack polynomials with prescribed symmetry and some of their clustering properties
• Odd Dunkl Operators and nilHecke Algebras