Schur-Sergeev duality for Ariki-Koike algebras

2018/08/26 by Deke Zhao, Zhao, Deke
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1808.08484

openalex publication_date 2018/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U_q(\mathfrakg) be the quantized superalgebra of \mathfrakg=\mathfrakgl(k₁|ℓ₁)⊕⋯⊕\mathfrakgl(k_m|ℓ_m) and H_m,n(q,Q) the cyclotomic Hecke algebra of type G(m,1,n). We define a right H_m,n(q,Q)-action on the n-fold tensor (super)space of the vector representation of U_q(\mathfrakg) and prove the Schur--Weyl reciprocity between U_q(\mathfakg) and H_m,n(q,Q).

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