Separation of variables in the $A_2$ type Jack polynomials

V. B. Kuznetsov; E. K. Sklyanin

Separation of variables in the $A_2$ type Jack polynomials

solv-int 2015-11-13 v1 Quantum Algebra Exactly Solvable and Integrable Systems q-alg

Authors: V. B. Kuznetsov , E. K. Sklyanin

Abstract

An integral operator $M$ is constructed performing a separation of variables for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of $M$ the CS eigenfunctions (Jack polynomials for the root system $A_2$ ) are transformed to the factorized form $\phi(y_1)\phi(y_2)$ , where $\phi(y)$ is a trigonometric polynomial of one variable expressed in terms of the ${}_3F_2$ hypergeometric series. The inversion of $M$ produces a new integral representation for the $A_2$ Jack polynomials.

Keywords

calogero models special functions operator theory and quantum mechanics

Cite

@article{arxiv.solv-int/9508002,
  title  = {Separation of variables in the $A_2$ type Jack polynomials},
  author = {V. B. Kuznetsov and E. K. Sklyanin},
  journal= {arXiv preprint arXiv:solv-int/9508002},
  year   = {2015}
}

Comments

17 pages, LATEX, macros included, no figures

Separation of variables in the $A_2$ type Jack polynomials

Abstract

Keywords

Cite

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