Abstract

The purpose of this paper is to survey some of the main results and techniques from the transformation theory of U(n + 1) multiple basic hypergeometric series associated to the root system An. Our approach to this theory employs partial fraction decompositions, q-difference equations, and suitable multidimensional matrix inversions. These series were strongly motivated by Biedenharn and Louck and coworkers mathematical physics research involving angular momentum theory and the unitary groups U(n + 1), or equivalently An. The foundation of our theory is the U(n + 1) multiple sum renement of the terminating classical q-binomial theorem. This result contains as special, limiting, or transformed cases both the Macdonald identities for An, and U(n + 1) multiple sum extensions of the classical q-binomial theorem, Ramanujan's 1 1 sum, the balanced 3 2 summation theorem, and Rogers ' classical terminating very-well-poised 6 5 summation

Citations