The authors extend the classical Schur-Weyl duality to the quantum affine case. In other words, they first “quantize” the setup by replacing the general linear group \(\text{GL}_ n\) by the quantized universal enveloping algebra of \({\mathfrak {gl}}_ n\) and the symmetric group \(S_ d\) by the Hecke algebra of type \(A_ d\). Then they “affinize” by replacing the field of complex numbers by the \(p\)-adic field.
The approach used is geometric. In fact, the polynomial tensor representations which play the role of the tensor powers of the natural representation for \(\text{GL}_ n\) in the classical setup is produced by three different geometric constructions. The first is based on equivariant \(K\)-theory, the two others involve the affine flag variety over finite fields.
For the entire collection see [Zbl 0801.00049].