# Jack Polynomials and the Multi-Component Calogero-Sutherland Model

@article{Forrester1996JackPA, title={Jack Polynomials and the Multi-Component Calogero-Sutherland Model}, author={Peter J. Forrester}, journal={International Journal of Modern Physics B}, year={1996}, volume={10}, pages={427-441} }

Using the ground state ψ0 of a multi-component generalization of the Calogero-Sutherland model as a weight function, orthogonal polynomials in the coordinates of one of the species are constructed. Using evidence from exact analytic and numerical calculations, it is conjectured that these polynomials are the Jack polynomials where λ is the coupling constant. The value of the normalization integral for is conjectured, and some further related integrals are evaluated.

## 7 Citations

The Yangian symmetry in the spin Calogero model and its applications

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- 1997

By using the non-symmetric Hermite polynomials and a technique based on the Yangian Gelfand - Zetlin bases, we decompose the space of states of the Calogero model with spin into irreducible Yangian…

The Calogero-Sutherland model and polynomials with prescribed symmetry

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- 1997

Abstract The Schrodinger operators with exchange terms for certain Calogero-Sutherland quantum many-body systems have eigenfunctions which factor into the symmetric ground state and a multivariable…

The orthogonal eigenbasis and norms of eigenvectors in the spin Calogero - Sutherland model

- Mathematics, Physics
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Using a technique based on the Yangian Gelfand - Zetlin algebra and the associated Yangian Gelfand - Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero - Sutherland model…

Generalized weight functions and the Macdonald polynomials

- Mathematics
- 1996

A weight function which $q$-generalizes the ground state wave function of the multi-component Calogero-Sutherland quantum many body system is introduced. Conjectures, and some proofs in special…

Jack vertex operators and realization of Jack functions

- Mathematics
- 2014

We give an iterative method to realize general Jack functions using vertex operators. We first prove some cases of Stanley’s conjecture on positivity of the Littlewood–Richardson coefficients, and…

New algebraic quantum many-body problems

- Mathematics, Physics
- 2000

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly solvable models include…

Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras

- Physics
- 2009

We present a general method to obtain the central charge and quasihole scaling dimension directly from groundstate and quasihole wavefunctions. Our method applies to wavefunctions satisfying specific…

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