Nichols algebras and Kazhdan Lusztig correspondences

Abstract: To any object in a braided tensor category we can associate a Nichols algebra, either through braid group combinatorics or through a universal property. The main motiviation for Nichols algebras is to systematically construct the quantum group from its Cartan part, but it can be used to construct many novel braided tensor categories with interesting root system structure. In conformal field theory, braidings appear as monodromies of certain differential equations such as the Knizhnik–Zamolochikov equation. The Kazhdan–Lusztig correspondence links the representation theory appearing in such conformal field theories to quantum groups. Using Nichols algebras and other categorical tools, we have recently proven a nonsemisimple version of this result conjectured by Feigin et al. In our most recent work, we determine the braided tensor category of modules of affine sl(2) at admissible level in terms of a quantum group of type sl(2|1).

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.