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

Let be the quantized universal enveloping algebra of . Let θ be the automorphism of which is defined on generators by Ei↦Ei−m, Fi↦Fi−m, Kj↦Kj−m for any 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 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].