  An inductive approach to the representation theory of the chain of the
complex reflection groups G(m,1,n) is presented. We obtain the Jucys-Murphy
elements of G(m,1,n) from the Jucys--Murphy elements of the cyclotomic Hecke
algebra, and study their common spectrum using representations of a degenerate
cyclotomic affine Hecke algebra. Representations of G(m,1,n) are constructed
with the help of a new associative algebra whose underlying vector space is the
tensor product of the group ring of G(m,1,n) with a free associative algebra
generated by the standard m-tableaux.
