Joseph ideals and lisse minimal W-algebras

TL;DR

This paper constructs new lisse W-algebras by lifting Joseph ideals to affine Kac-Moody algebras, revealing novel examples of vertex algebras with minimal nilpotent orbit closures as their associated varieties.

Contribution

It introduces a new method of lifting Joseph ideals to affine Kac-Moody algebras, producing previously unknown lisse W-algebras not derived from admissible representations.

Findings

New affine vertex algebras with minimal nilpotent orbit closures as associated varieties

Identification of a new family of lisse ($C_2$-cofinite) W-algebras

Examples of W-algebras not arising from admissible representations

Abstract

We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac-Moody algebras and find new examples of affine vertex algebras whose associated varieties are minimal nilpotent orbit closures. As an application we obtain a new family of lisse ($C_2$-cofinite) W-algebras that are not coming from admissible representations of affine Kac-Moody algebras.