Emmy-Noether-Seminar: On the structure of W-algebras

On the structure of W-algebras

Shigenori Nakatsuka (FAU)

Abstract: The W-algebras are vertex algebras obtained from affine Lie algebras through quantized Drinfeld-Sokolov reductions parametrized by nilpotent orbits. They are fundamental objects for studying Whittaker models for affine Lie algebras. Recently, it has been conjectured that the W-algebras are organized along the closure relations of nilpotent orbits: more precisely, two W-algebras should be reconstructed from each other if the corresponding two nilpotent orbits are in closure relations. In this talk, I will discuss the motivation, the current status of this conjecture, and various applications to the representation theory. The talk is based on several joint works with Creutzig-Fasquel-Linshaw, Fasquel-Fehily-Fursman, and Fasquel-Kovalchuk.