Abstract

We prove a Schur–Weyl duality between the quantum enveloping algebra of ${\mathfrak{𝔤}\mathfrak{𝔩}}_m$ and certain quotient algebras of Ariki–Koike algebras, which we describe explicitly. This duality involves several algebraically independent parameters and the module underlying it is a tensor product of a parabolic universal Verma module and a tensor power of the standard representation of ${\mathfrak{𝔤}\mathfrak{𝔩}}_m$. 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 special case of our algebras.

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