Seminar for Algebra

On Friday, March 14, 2025, 14:00 hours, lecture room 104, Nakatsuka Shigenori (FAU Erlangen-Nurnberg) will hold lecture as part of Seminar for Algebra titled:

On the structure of W-algebras.

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 to study the representation theory of 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 some applications to representation theory. The talk is based on several joint works with Creutzig-Fasquel-Linshaw, and Fasquel-Kovalchuk.