A note on a generalization of Macdonald’s identities forA l andB l

Abstract

Al~trJet. Let r/(q) denote the Dedekind's ~-function. Macdonald obtainod identitics for t/(q) di'~ where 9 is complex simple finite dimensional Lie algebra. The aim of this paper is to obtain generalization of the above identities in the case of g = At and Be. We also get new formulas for the generating functions of the Ramanujan's r-function and 0,-functions. KeywotdL Macdonald's multivariable identities; Dcdekind's eta function;