Simplicity of higher rank triplet W-algebras

Abstract

We show that the higher rank triplet W-algebra is simple when p is bigger than or equal to h-1. Furthermore, we show that the Feigin-Tipunin's module over the higher rank triplet W-algebra introduced in arXiv:1002.5047 is simple if the parameter is in the closure of the fundamental alcove, and give the decomposition as a direct sum of simple modules over the affine W-algebras at level p-h.

19 pages, to appear in IMRN

References in corpus (6)

• Logarithmic extensions of minimal models: characters and modular transformations
• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity
• Logarithmic CFTs connected with simple Lie algebras
• The N=1 triplet vertex operator superalgebras
• The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
• Generalized Vertex Algebras

Cited by in corpus (1)

• Quasi-lisse extension of affine ${\mathfrak{sl}}_2$ à la Feigin--Tipunin