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 $\mathbb{C}G(m,1,n)$ with a free associative algebra generated by the standard $m$-tableaux.