Highest weight Macdonald and Jack Polynomials

Abstract

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.

17 pages, published version

References in corpus (5)

• Fractional Quantum Hall States and Jack Polynomials
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras

Cited by in corpus (9)

• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Jack polynomial fractional quantum Hall states and their generalizations
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
• Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid
• Vector-Valued Jack Polynomials from Scratch
• Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
• Vector valued Macdonald polynomials
• Graphical Calculus for the Double Affine Q-Dependent Braid Group
• Singular Nonsymmetric Macdonald Polynomials and Quasistaircases