A new map predicts the associated variety of every simple affine vertex algebra at integer levels above criticality as a single sheet, with compatibility theorems connecting it to reduction types and affine cells.
Introduction to W-algebras and their representation theory
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abstract
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy. December 9, 2014 -- February 28, 2015.
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Cyclotomic level maps and associated varieties of simple affine vertex algebras
A new map predicts the associated variety of every simple affine vertex algebra at integer levels above criticality as a single sheet, with compatibility theorems connecting it to reduction types and affine cells.