TITLE: Reference for quantum Schur-Weyl duality
QUESTION [5 upvotes]: I am trying to prove a version of quantum Schur-Weyl duality. I hope to be able to generalize the proof of the Schur-Weyl duality between $U_q(\mathfrak{gl}_n)$ and the Hecke algebra $H_r$. So I am looking for a good reference for this with a careful proof. It would also be nice to see a proof that uses the quantum coordinate ring of $GL_n$ instead of the enveloping algebra (and therefore is phrased in terms of decomposing $V^{\otimes r}$ as a left-comodule for this coordinate ring and a right $H_r$-module).

REPLY [2 votes]: Too late maybe but still - "Noncommutative symmetric functions V: a degenerate version of $U_q(\mathfrak{gl}_N)$" by Krob and Thibon has the quantum coordinate ring version very carefully (I think) written. It is aimed at the $q=0$ case but the generic $q$ is treated in detail too.
Later - found the book "Algebras of Functions on Quantum Groups" by Korogodski and Soibelman (1998), it contains a thorough description of the quantization of algebras of functions on groups.