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arXiv · 2606.08990

Associated varieties of simple affine vertex algebras at rational levels

Peng Shan·Wenbin Yan·Qixian Zhao
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Abstract

We present a conjecture for associated varieties of simple affine vertex algebras $L_k(\mathfrak{g})$ attached to a simple Lie algebra $\mathfrak{g}$ 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.

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Peng Shan, Wenbin Yan, Qixian Zhao. 2026-06-08. Associated varieties of simple affine vertex algebras at rational levels. https://arxiv.org/abs/2606.08990

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