  We prove a Schur-Weyl duality between the quantum enveloping algebra of
$\mathfrak{gl}_m$ and certain quotient algebras of Ariki-Koike algebras, which
we give explicitly. The duality involves several algebraically independent
parameters and is realized through the tensor product of a parabolic universal
Verma module and a tensor power of the natural representation of
$\mathfrak{gl}_m$. We also give a new presentation by generators and relations
of the generalized blob algebras of Martin and Woodcock as well as an
interpretation in terms of Schur-Weyl duality by showing they occur as a
particular case of our algebras.
