  Let F be a global function field and let F^ab be its maximal abelian
extension. Following an approach of D.Hayes, we shall construct a continuous
homomorphism \rho: Gal(F^ab/F) \to C_F, where C_F is the idele class group of
F. Using class field theory, we shall show that our \rho is an isomorphism of
topological groups whose inverse is the Artin map of F. As a consequence of the
construction of \rho, we obtain an explicit description of F^ab. Fix a place
\infty of F, and let A be the subring of F consisting of those elements which
are regular away from \infty. We construct \rho by combining the Galois action
on the torsion points of a suitable Drinfeld A-module with an associated
\infty-adic representation studied by J.-K. Yu.
