Separation of variables in the $A_2$ type Jack polynomials

Details Separation of variables in the $A_2$ type Jack polynomials Separation of variables in the $A_2$ type Jack polynomials

1995-08-21

arxiv.org/abs/solv-int/9508002v1

Mathematics

Quantum Algebra

17 pages, LATEX, macros included, no figures

Scientific paper

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.

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