The automorphisms of affine fusion rings.

zbMath1053.17017arXivmath/0002044MaRDI QIDQ1597986

Terry Gannon

Publication date: 15 June 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0002044

zbMATH Keywords

conformal field theoryvertex operator algebrasS-matrixDynkin diagramsaffine algebrasfusion ringsKac-Petersen matrix

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) 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)

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Auto-equivalences of the modular tensor categories of type \(A, B, C\) and \(G\) ⋮ Modular data: the algebraic combinatorics of conformal field theory ⋮ Fusion algebras for imprimitive complex reflection groups. ⋮ Reconstructing braided subcategories of \(SU (N)_k \) ⋮ Bases of Feigin-Stoyanovsky's type subspaces for \(C_\ell ^{(1)}\) ⋮ Prime decomposition of modular tensor categories of local modules of type D ⋮ Lie theory for fusion categories: A research primer ⋮ Fusion algebras with negative structure constants. ⋮ Bases of standard modules for affine Lie algebras of type ⋮ Equivalences of graded fusion categories ⋮ Boundary conformal field theory and fusion ring representations ⋮ Simple current auto-equivalences of modular tensor categories ⋮ Integral modular data and congruences. ⋮ Weight-lattice discretization of Weyl-orbit functions

Cites Work

• Conformal field theory
• Quantum groups, quantum categories and quantum field theory
• Littlewood-Richardson coefficients for Hecke algebras at roots of unity
• New exceptional modular invariant partition functions for simple Kac- Moody algebras
• Fusion rules and modular transformations in 2D conformal field theory
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Modular and conformal invariance constraints in representation theory of affine algebras
• Simple WZW currents
• Fusion rule engineering
• Exotic Fourier transform
• Symmetries of the Kac-Peterson modular matrices of affine algebras
• An equivalence of fusion categories
• Automorphism modular invariants of current algebras
• Intertwining operator algebras and vertex tensor categories for affine Lie algebras
• On axiomatic approaches to vertex operator algebras and modules
• Quantum invariants of knots and 3-manifolds
• Finite group modular data
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