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Woronowicz Tannaka-Krein duality and free orthogonal quantum groups

Sara Malacarne


Given a finite-dimensional Hilbert space $H$ and a collection of operators between its tensor powers satisfying certain properties, we give a short proof of the existence of a compact quantum group $G$ with a fundamental representation $U$ on $H$ such that the intertwiners between the tensor powers of $U$ coincide with the given collection of operators. We then explain how the general version of Woronowicz Tannaka-Krein duality can be deduced from this.

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