For every l >= 5, the vacuum block of the level -1 simple affine vertex algebra of type D_l has exactly l+1 irreducible modules, indexed by a subregular Kazhdan-Lusztig left cell.
Affine vertex algebras and an affine analog of Barbasch-Vogan's construction
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This is an expository paper based on the authors' joint works. The goal is to explain the statements and the ideas behind two conjectures on associated varieties and simple modules of simple affine vertex algebras $L_k(\mathfrak{g})$ for a simple and simply-laced Lie algebra $\mathfrak{g}$ and a integer level $k$ above the critical level.
fields
math.QA 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Subregular affine cells and the level $-1$ vertex algebra of type $D$
For every l >= 5, the vacuum block of the level -1 simple affine vertex algebra of type D_l has exactly l+1 irreducible modules, indexed by a subregular Kazhdan-Lusztig left cell.