2022/12/29 by Dražen Adamović, Ching Hung Lam, Adamovic, Drazen +5 · 1 citation
Mathematics · Physics and Astronomy · #17B67 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2212.14137
openalex publication_date 2022/12/29 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28
In arXiv:1811.04649, we extended the Dong-Mason theorem on irreducibility of modules for cyclic orbifold vertex algebras to the entire category weak modules and applied this result to Whittaker modules. In this paper we present further generalizations of these results for nonabelian orbifolds of vertex operator superalgebras. Let V be a vertex superalgebra with a countable dimension and let G be a finite subgroup of Aut(V). Assume that h∈ Z(G) where Z(G) is the center of the group G. For any irreducible h-twisted (weak) V-module M, we prove that if M\not≅ g∘ M for all g∈ G then M is also irreducible as VG-module. We also apply this result to examples and give irreducibility of modules of Whittaker type for orbifolds of Neveu-Schwarz vertex superalgebras, Heisenberg vertex algebras, Virasoro vertex operator algebra and Heisenberg-Virasoro vertex algebra.