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Abstract: We show that under suitable assumptions, we have a one-to-one correspondencebetween classical groups and free quantum groups, in the compact orthogonalcase. We classify the groups under correspondence, with the result that thereare exactly 6 of them: $O n,S n,H n,B n,S n-,B n-$. We investigate therepresentation theory aspects of the correspondence, with the result that for$O n,S n,H n,B n$, this is compatible with the Bercovici-Pata bijection.Finally, we discuss some more general classification problems in the compactorthogonal case, notably with the construction of a new quantum group.



Author: Teodor Banica, Roland Speicher

Source: https://arxiv.org/



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