Moritz Weber (Saarland) 23 November 2021

Easy quantum groups and quantum permutations

Within Woronowicz’s framework of compact quantum groups, there are natural quantum analogs of the symmetric group, the orthogonal group and the unitary group, amongst others. They have in common that their representation theory may be expressed in terms of diagrams. This has been systematically formalized by Banica and Speicher in 2009 within the class of so called „easy“ quantum groups.We give an introduction to „easy“ quantum groups, their diagrammatic representation theory and we mention some links with Deligne’s interpolation categories. Moreover, we highlight the role of quantum permutations within the theory of quantum automorphism groups of graphs. This also links with nonlocal games in quantum information theory, as we will point out.