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In the paper by Chari and Pressley, it is proved that the there is functor from the category $C_m$ of finite dimensional representations of the affine Hecke algebra of $GL(m)$ to the category $D_n$ of finite dimensional representations of $U_q(\widehat{sl}_n)$.

$U_q(\widehat{sl}_n)$ is type A quantum affine algebra. Are there some references about similar results of quantum affine algebras of other types? Thank you very much.

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  • $\begingroup$ Historically, the Frobenius-Schur duality between the Yangian $Y(\mathfrak{sl}_n)$ and the degenerate affine Hecke algebra appeared first, so one could also pose this question for Yangians (hoping that some progress has been made there). Unfortunately (to my knowledge), I don't think this has been explored beyond the case where $\mathfrak{g}$ is type A. (If I am wrong about this I would love to see a reference!) $\endgroup$
    – CWsl2
    Commented Nov 1, 2016 at 21:03

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