Let $S$ be the spinor representation of $U_qmathfrak{so}_N$, for $N$ odd and $q^2$ not a rooot of unity. We show that the commutant of its action on $S^{otimes n}$ is given by a representation of the nonstandard quantum group $U_{-q^2}mathfrak{so}_n$. For $N$ even, an analogous statement also holds for $S=S_+oplus S_-$ the direct sum of the irreducible spinor representations of $U_qmathfrak{so}_N$, with the commutant given by $U_{-q}mathfrak{o}_n$, a $mathbb{Z}/2$-extension of $U_{-q}mathfrak{so}_n$. Similar statements also hold for fusion tensor categories with $q$ a root of unity.
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