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Journal Articles Pacific Journal of Mathematics Year : 2021

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

Abstract

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 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 $\mathfrak{gl}_m$. 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 special case of our algebras.
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Dates and versions

hal-04225924 , version 1 (03-10-2023)

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Abel Lacabanne, Pedro Vaz. Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras. Pacific Journal of Mathematics, 2021, 311 (1), pp.113-133. ⟨10.2140/pjm.2021.311.113⟩. ⟨hal-04225924⟩
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