Bisymmetric functions, Macdonald polynomials and Sl(3) basic hypergeometric series

A new type Of sl(3) basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key ingredient in the 513 basic hypergeometric series is a bisymmetric function related to Macdonald's commuting family of q-difference operators, to the sl(3) Selberg integrals of Tarasov and Varchenko, and to alternating sign matrices. Our main result for sl(3) series is a multivariable generalization of the celebrated q-binomial theorem. In the limit this q-binomial sum yields a new sl(3) Selberg integral for Jack polynomials.