Associated varieties of simple affine vertex algebras at rational levels

2026/06/08 by Peng Shan, Wenbin Yan, Qixian Zhao
#math.RT

paper · pdf

Abstract

We present a conjecture for associated varieties of simple affine vertex algebras L_k(\mathfrakg) attached to a simple Lie algebra \mathfrakg of simply-laced type and any rational level k greater than the critical level. The key new ingredient compared to the integral case is the covering duality map introduced by Gao-Liu-Lo-Shahidi. We provide evidence for the conjecture.

Related

• Cyclotomic level maps and associated varieties of simple affine vertex algebras
• Associated Varieties of Ordinary Modules over Quasi-Lisse Vertex Algebras
• Vertex operator algebras associated to modified regular representations of affine Lie algebras
• The varieties of semi-conformal vectors of affine vertex operator algebras
• Fusion categories for affine vertex algebras at admissible levels