Schur–Weyl reciprocity between quantum groups and Hecke algebras of type G(p,p,n)

AbstractLet Uq(glm⊕p) be the quantized universal enveloping algebra of glm⊕p. Let θ be the automorphism of Uq(glm⊕p) which is defined on generators by Ei↦Ei−m, Fi↦Fi−m, Kj↦Kj−m for any i∈Z/pmZ∖{0¯,m¯,…,(p−1)m¯} and any j∈Z/pmZ. Let H(p,p,n) be the Hecke algebra of type G(p,p,n) with parameters q,ε, where ε is a primitive pth root of unity. In this paper we establish a Schur–Weyl reciprocity between H(p,p,n) and a twisted tensor product of Uq(glm⊕p) and the group algebra for 〈θ〉 (a cyclic group of order p) by using the results in [J. Hu, J. Algebra 274 (2004) 446–490]