Multiple basic hypergeometric transformation formulas arising from the balanced duality transformation

Abstract: Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking certain limits of the balanced duality transformation. By combining some of them, some transformation formulas for $A_n$ basic hypergeometric series is given. They include some generalizations of Watson, Sears and ${}_8 W_7$ transformations.