Elsevier

Advances in Mathematics

Volume 222, Issue 4, 10 November 2009, Pages 1461-1501
Advances in Mathematics

Liberation of orthogonal Lie groups

https://doi.org/10.1016/j.aim.2009.06.009Get rights and content
Under an Elsevier user license
open archive

Abstract

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: On, Sn, Hn, Bn, Sn, Bn. We investigate the representation theory aspects of the correspondence, with the result that for On, Sn, Hn, Bn, 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.

MSC

16W30
46L54

Keywords

Quantum group
Noncrossing partition

Cited by (0)