A_2 Macdonald polynomials: a separation of variables

Abstract

In this paper we construct a discrete linear operator $K$ which transforms $A_2$ Macdonald polynomials into the product of two basic $3{\varphi }_2$ hypergeometric series with known arguments. The action of the operator $K$ on power sums in two variables can be reduced to a generalization of one particular case of the Bailey's summation formula for a very-well-poised $6{\psi }_6$ series. We also propose the conjecture for a transformation of $6{\psi }_6$ series with different arguments.

17 pages, LaTeX, no figures

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