AbstractA powerful technique in representation theory is localization, wherein one identifies categories of modules for an algebra of interest with categories of D-modules or perverse sheaves. After reviewing the classical Beilinson”ŖBernstein theorem, which introduced localization for semisimple Lie algebras, we will describe some analogues for certain vertex algebras, notably W-algebras and...
The geometric Satake correspondence has played a central role in the geometric Langlands program. It is indispensable for the construction of global Langlands correspondences over globa function fields (by Vincent Lafforgue) and for the geometrization of the local Langlands correspondence over local fields (by Laurent Fargues and Peter Scholze). It is a categorical lifting of the classical Sata...