Speaker: Bernardo Zan (U. Genoa)
Title: Quantum groups as global symmetries
Abstract: Quantum groups are algebras which have been known to describe the symmetry of certain lattice systems. In the continuum, instead, they seem to play a different and more subtle role, appearing in two-dimensional CFTs in a more indirect manner; in the literature, they are sometimes referred to as “hidden symmetries”. I'll elucidate the role of quantum groups as global symmetries in the continuum by considering CFTs which have the quantum group as a bona fide global symmetry; I will discuss this question in the case of the simplest quantum group Uq(sl2), giving both the general picture and studying a specific example arising from the continuum limit of a lattice model. I will discuss the consequences of this symmetry, and how this is related to some of those ordinary theories (e.g. minimal models) where quantum groups are known to appear indirectly.