An elementary proof of the Macdonald identities for A(1)l

Abstract

AbstractIn this paper it is shown that the Macdonald identities for A(1)l are a natural consequence of the recent multivariable generalization of classical basic hypergeometric series known as basic hypergeometric series in U(n). More precisely, a U(n) multiple series generalization of the q-binomial theorem is derived and used to generalize Cauchy's elegant proof of Jacobi's triple product identity and to give a direct, elementary proof of the Macdonald identities for A(1)l