This goes back to Jimbo I think. A reference is:
"A q-difference analogue of $U(mathfrak g)$, Hecke algebra and the Yang-Baxter equation'', Lett. Math. Phys. 11 (1986).
It has been much studied though, so there are lots of subsequent papers, some of which might be closer to what you are looking for? For example this paper studies an analogue of Schur-Weyl duality for "walled Brauer algebras", and this paper studies a two-parameter version.
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