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Nov 1, 2016 at 21:03 comment added CWsl2 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!)
Oct 16, 2016 at 9:01 history asked Jianrong Li CC BY-SA 3.0