Schur-Sergeev duality for Ariki-Koike algebras

Abstract

Let $U_q(\mathfrak{g})$ be the quantized superalgebra of $\mathfrak{g}=\mathfrak{gl}(k_1|{\ell }_1)\oplus \cdots \oplus \mathfrak{gl}(k_m|{\ell }_m)$ and $H_{m,n}(q,\mathbf{Q})$ the cyclotomic Hecke algebra of type $G(m,1,n)$. We define a right $H_{m,n}(q,\mathbf{Q})$-action on the $n$-fold tensor (super)space of the vector representation of $U_q(\mathfrak{g})$ and prove the Schur--Weyl reciprocity between $U_q(\mathfak{g})$ and $H_{m,n}(q,\mathbf{Q})$.

Title changed, Some typos fixed and other minor changes