Coset Vertex Operator Algebras and \W-Algebras

2017/01/24 by Tomoyuki Arakawa, Arakawa, Tomoyuki, Cuipo Jiang +1 · 1 citation
Mathematics · #17B69 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B69

paper · pdf · doi:10.48550/arxiv.1701.06880

21 pages

arxiv created 2017/01/24 · openalex publication_date 2017/01/24 · arxiv updated 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit description for the weight three generator of the coset vertex operator algebra C_L_\widehat\sl_n(l,0)⊗ L_\widehat\sl_n(1,0)(L_\widehat\sl_n(l+1,0)), for n≥ 2, l≥ 1. Furthermore, we prove that the commutant C_L_\widehat\sl₃(l,0)⊗ L_\widehat\sl₃(1,0)(L_\widehat\sl₃(l+1,0)) is isomorphic to the \W-algebra \W_{-3+(l+3)/(l+4)}(\sl₃), which confirms the conjecture for the \sl₃ case that C_L_\widehat\frak g(l,0)⊗ L_\widehat\frak g(1,0)(L_\widehat\frak g(l+1,0)) is isomorphic to \W_{-h+(l+h)/(l+h+1)}(\frak g) for simply-laced Lie algebras \frak g with its Coxeter number h for a positive integer l.

Citations

• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras

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• Singular vectors for the WN algebras

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