Schur–Weyl duality, Verma modules, and row quotients of Ariki–Koike algebras

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