Vol. 247, No. 1, 2010

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Classification results for easy quantum groups

Teodor Banica, Stephen Curran and Roland Speicher

Vol. 247 (2010), No. 1, 1–26

We study the orthogonal quantum groups satisfying the “easiness” assumption axiomatized in our previous paper, with the construction of some new examples and with some partial classification results. The conjectural conclusion is that the easy quantum groups consist of the previously known 14 examples, plus a hypothetical multiparameter “hyperoctahedral series”, related to the complex reflection groups Hns = s Sn. We also discuss the general structure and the computation of asymptotic laws of characters for the new quantum groups that we construct.

quantum group, noncrossing partition
Mathematical Subject Classification 2000
Primary: 46L65
Secondary: 20F55, 46L54
Received: 21 June 2009
Accepted: 15 January 2010
Published: 1 July 2010
Teodor Banica
Department of Mathematics
Cergy-Pontoise University
95000 Cergy-Pontoise
Stephen Curran
Department of Mathematics
University of California
Berkeley, CA 94720
United States
Roland Speicher
Department of Mathematics and Statistics
Queen’s University
Jeffery Hall
Kingston, Ontario K7L 3N6