  This paper gives a Schur-Weyl duality approach to the representation theory
of the affine Hecke algebras of type C with unequal parameters. The first step
is to realize the affine braid group of type $C_k$ as the group of braids on
$k$ strands with two poles. Generalizing familiar methods from the one pole
(type A) case, this provides commuting actions of the quantum group
$U_q\mathfrak{g}$ and the affine braid group of type $C_k$ on a tensor space
$M\otimes N \otimes V^{\otimes k}$. Special cases provide Schur-Weyl pairings
between the affine Hecke algebra of type $C_k$ and the quantum group of type
$\mathfrak{gl}_n$, resulting in natural labelings of many representations of
the affine Hecke algebras of type C by partitions. Following an analysis of the
structure of weights of affine Hecke algebra representations (extending the one
parameter case to the three parameter case necessary for affine Hecke algebras
of type C), we provide an explicit identification of the affine Hecke algebra
representations that appear in tensor space (essentially by identifying their
Langlands parameters).
