Emmy-Noether-Seminar: Proving the logarithmic Kazhdan Lusztig conjecture

Proving the logarithmic Kazhdan Lusztig conjecture

Simon Lentner (Hamburg)

Abstract: I will review qualitatively how braidings and Nichols algebras appear in conformal field theory. Then I present our recent proof of the logarithmic Kazhdan Lusztig conjecture: This conjecture roughly 20 years ago by Feigin et. al. state that certain vertex algebras have a representation category equivalent to the representation category of a quantum group. The proof strategy is essentially algebraic and interesting in its own right, it states that braided tensor categories of a certain type have to necessarily come from generalized quantum groups.