The ``strange'' Lie superalgebra \(q(n)\) is unfriendly in several ways: The Cartan subalgebra is not purely even, there is no invariant bilinear form and no quadratic Casimir operator. In some other respects the algebra has properties analogous to those of the general linear algebra \(\text{gl}(n)\). For example, there is a remarkable analogue of the Schur- Weyl duality --- this is the representation theoretic duality between the reduction of the \(N\)th tensor power of the self-representation of \(\text{gl}(n)\) and the representations of \(S(N)\), the symmetric group on \(N\) letters. In this paper, the author reports a \(q\)-version of this duality involving the quantized universal enveloping algebra of \(q(n)\) and an extension \(HC_ q(N)\) of the Hecke algebra \(H_ q(N)\).