Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series

Abstract

A one-parameter generalisation R_{\lambda}(X;b) of the symmetric Macdonald polynomials and interpolations Macdonald polynomials is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal specialisation formula and q-difference equation for R_{\lambda}(X;b). We also prove a new multiple q-Gauss summation formula and several further results for sl_n basic hypergeometric series based on R_{\lambda}(X;b).