2022/06/07 by Haisheng Li, Jiancai Sun, Li, Haisheng +1 · 2 citations
Mathematics · #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2206.03455
openalex publication_date 2022/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is to study what we call twisted regular representations for vertex operator algebras. Let V be a vertex operator algebra, let σ1,σ2 be commuting finite-order automorphisms of V and let σ=(σ1σ2)-1. Among the main results, for any σ-twisted V-module W and any nonzero complex number z, we construct a weak σ1⊗ σ2-twisted V⊗ V-module \mathfrakDσ1,σ2(z)(W) inside W*. Let W1,W2 be σ1-twisted, σ2-twisted V-modules, respectively. We show that P(z)-intertwining maps from W1⊗ W2 to W* are the same as homomorphisms of weak σ1⊗ σ2-twisted V⊗ V-modules from W1⊗ W2 into \mathfrakDσ1,σ2(z)(W). We also show that a P(z)-intertwining map from W1⊗ W2 to W* is equivalent to an intertwining operator of type \binomW'W1 W2, which is a twisted version of a result of Huang and Lepowsky. Finally, we show that for each τ-twisted V-module M with τ any finite-order automorphism of V, the coefficients of the q-graded trace function lie in \mathfrakDτ,τ-1(-1)(V), which generate a τ⊗ τ-1-twisted V⊗ V-submodule isomorphic to M⊗ M'.