THE A l AND C l BAILEY TRANSFORM

Abstract. We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative “Bailey chain” concept in the setting of basic hypergeometric series very well-poised on unitary Al or symplectic Cl groups. The classical case, corresponding to A1 or equivalently U(2), contains an immense amount of the theory and application of one-variable basic hypergeometric series, including elegant proofs of the Rogers-Ramanujan-Schur identities. In particular, our program extends much of the classical work of Rogers, Bailey, Slater, Andrews, and Bressoud.