Joseph ideals and lisse minimal W-algebras

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.

References and comments added in the introduction. Proof of Theorem 4.2 slightly correct. Conjecture 2 and 4 are corrected

References in corpus (1)

• Infinite Chiral Symmetry in Four Dimensions

Cited by in corpus (29)

• Vertex operator algebras, Higgs branches, and modular differential equations
• Surface Defects and Chiral Algebras
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural results
• Trialities of $\mathcal{W}$-algebras
• Magnetic quivers for rank 2 theories
• The exact Schur index in closed form
• Tensor categories of affine Lie algebras beyond admissible levels
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• On the chiral algebra of Argyres-Douglas theories and S-duality
• Universal two-parameter even spin ${\mathcal{W}}_{\infty }$-algebra
• Rationality and Fusion Rules of Exceptional W-Algebras
• An application of collapsing levels to the representation theory of affine vertex algebras
• Surface defects, flavored modular differential equations and modularity
• Finite vs infinite decompositions in conformal embeddings
• Introduction to W-algebras and their representation theory
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• Sheets and associated varieties of affine vertex algebras
• Arc spaces and chiral symplectic cores
• Hidden exceptional symmetry in the pure spinor superstring
• Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras
• Representation theory of W-algebras and Higgs branch conjecture
• Associated varieties and Higgs branches (a survey)
• Free field realisation and the chiral universal centraliser
• On rationality for $C_2$-cofinite vertex operator algebras
• Simplicity of vacuum modules and associated varieties
• On the representation theory of the vertex algebra $L_{-5/2}(sl(4))$
• Unitarity of minimal $W$-algebras and their representations II: Ramond sector
• Associated varieties of simple affine VOAs $L_k(s{l}_3)$ and $W$-algebras $W_k(s{l}_3,f)$