On the classification of easy quantum groups - The nonhyperoctahedral and the half-liberated case

Details On the classification of easy quantum groups - The nonhyperoctahedral and the half-liberated case On the classification of easy quantum groups - The nonhyperoctahedral and the half-liberated case

2012-01-23

arxiv.org/abs/1201.4723v1

Mathematics

Operator Algebras

39 pages

Scientific paper

In 2009, Banica and Speicher began to study the compact quantum subgroups of the free orthogonal quantum group containing the symmetric group S_n. They focused on those whose intertwiner spaces are induced by some partitions. These so-called easy quantum groups have a deep connection to combinatorics. We continue their work on classifying these objects introducing some new examples of easy quantum groups. In particular, we show that the six easy groups O_n, S_n, H_n, B_n, S_n' and B_n' split into seven cases on the side of free easy quantum groups. Also, we give a complete classification in the half-liberated case.

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