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.
Minimal Reduction Type and Affine Springer Fibers
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abstract
We extend a result of Yun on minimal reduction types to the parahoric case. This implies a uniqueness property for 2-special representations appearing in the cohomology of certain affine Springer fibers. Using this, we settle a conjecture of Lusztig on strata in a reductive group.
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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.