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 the Kazhdan-Lusztig map
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one defined by Lusztig, and that the Kazhdan-Lusztig map is a section of our map. This settles several conjectures in the literature. For classical groups, we prove more refined results by introducing and studying the "skeleta" of affine Springer fibers.
fields
math.RT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.