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It is well-known that the commutant algebra of the $U_q(\mathfrak{sl}_2)$-action on the $n$-fold tensor product of its fundamental module is isomorphic to the Temperley-Lieb algebra TL$_n(\nu)$ with fugacity parameter $\nu = -q - q^{-1}$ (at least in the generic case, i.e., when $q$ is not a root of unity, or $n$ is small enough).
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