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.Comment: 39 pages; appeared in Advances in Mathematics, Vol. 245, pages
500-533, 201
Full text link
Get PDF
