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Mar 22 at 15:34 comment added Jules Lamers In particular, (Iwahori–)Hecke algebras appear naturally in both contexts: in number theory etc (related to $\mathbb{F}_q$; I don't know anything about this), and as the centraliser of $U_q \,\mathfrak{gl}_r$ on $V^{\otimes n}$ with $V=L_{\omega_1}$ in quantum Schur–Weyl duality.
Mar 22 at 13:59 history answered Alexander Chervov CC BY-SA 4.0