An explicit realization of logarithmic modules for the vertex operator algebra $\mathcal {W}_{p,p^{\prime }}$Wp,p′

DOI10.1063/1.4736424zbMath1276.81075arXiv1202.6667OpenAlexW3126119657MaRDI QIDQ2865543

Dražen Adamović, Antun Milas

Publication date: 29 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.6667

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Virasoro and related algebras (17B68) Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items

Characters of Modules of Irrational Vertex Algebras ⋮ Modular transformations and Verlinde formulae for logarithmic (\(p_+,p_-\))-models ⋮ Realizations of simple affine vertex algebras and their modules: the cases \({\widehat{sl(2)}}\) and \({\widehat{osp(1,2)}}\) ⋮ ${\mathbbm {C}}$ C -Graded vertex algebras and conformal flow ⋮ Classification of screening systems for lattice vertex operator algebras ⋮ C 2-Cofinite $\mathcal{W}$-Algebras and Their Logarithmic Representations

Cites Work

• The structure of Zhu's algebras for certain \(\mathcal W\)-algebras
• Graph fusion algebras of \({\mathcal WLM}((p,p')\)
• Coset graphs in bulk and boundary logarithmic minimal models
• On \(\mathcal W\)-algebra extensions of \((2,p)\) minimal models: \(p>3\)
• Logarithmic extensions of minimal models: characters and modular transformations
• Generalized twisted modules associated to general automorphisms of a vertex operator algebra
• \(\mathcal W\)-extended logarithmic minimal models
• Lattice construction of logarithmic modules for certain vertex algebras
• The physics superselection principle in vertex operator algebra theory
• A local logarithmic conformal field theory
• Logarithmic conformal field theories via logarithmic deformations
• On the triplet vertex algebra \(\mathcal W(p)\)
• On W-Algebras Associated to (2, p) Minimal Models and Their Representations
• Representation Theory of the Virasoro Algebra
• A modular invariant bulk theory for the \boldsymbol{c=0} triplet model
• Fusion of irreducible modules in {\cal WLM}(p,p^{\prime })
• Fusion rules of the {\cal W}_{p,q} triplet models
• Virasoro representations and fusion for general augmented minimal models
• Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models
• Integrable boundary conditions and {\cal W} -extended fusion in the logarithmic minimal models {\cal LM}(1\hbox{,}\, p)
• Logarithmic intertwining operators and W(2,2p−1) algebras