Cris Negron, UNC-Chapel Hill Mathematics Department – Geometric Methods of Representation Theory Seminar

Title: Modularization of quantum groups and some conformal field theory

Abstract: I will discuss recent work on constructing small quantum groups at even order roots of unity. (Recall that the small quantum group for a given simple Lie algebra is a characteristic 0, q-analog of its corresponding restricted enveloping algebra.) Our investigations are inspired by a conjectured equivalence of categories between representations for small quantum sl_2, at a certain even order parameter q, and representations for the so-called triplet conformal field theory. I will elaborate on this conjecture and explain how its resolution necessitates the introduction of certain “new” quantum groups, which are obtained from “old” quantum groups via deformation. No familiarity with quantum groups or conformal field theory will be assumed, and all relevant notions will be defined in the talk.