On the classification of easy quantum groups

In 2009, Banica and Speicher began to study the compact quantum groups G with Sn⊆G⊆On+ 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, by introducing some new examples of easy quantum groups. In particular, we show that the six easy groups On, Sn, Hn, Bn, Sn′ and Bn′ split into seven cases On+, Sn+, Hn+, Bn+, Sn′+, Bn′+ and Bn#+ on the side of free easy quantum groups. Also, we give a complete classification in the half-liberated and in the nonhyperoctahedral case.