Liberation of orthogonal Lie groups

Details Liberation of orthogonal Lie groups Liberation of orthogonal Lie groups

2008-08-19

arxiv.org/abs/0808.2628v2

Adv. Math. 222 (2009), 1461-1501

Mathematics

Quantum Algebra

42 pages

Scientific paper

We show that under suitable assumptions, we have a one-to-one correspondence between classical groups and free quantum groups, in the compact orthogonal case. We classify the groups under correspondence, with the result that there are exactly 6 of them: $O_n,S_n,H_n,B_n,S_n',B_n'$. We investigate the representation 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 compact orthogonal case, notably with the construction of a new quantum group.

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