An inductive approach to representations of complex reflection groups G( m, 1, n).

We propose an inductive approach to the representation theory of the chain of complex reflection groups G(m, 1, n). 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. We construct representations of G(m, 1, n) using a new associative algebra whose underlying vector space is the tensor product of the group ring ℂG(m, 1, n) with a free associative algebra generated by the standard m-tableaux. [ABSTRACT FROM AUTHOR]