Symmetries of the Kac-Peterson modular matrices of affine algebras

DOI10.1007/BF01231448zbMath0840.17021arXivq-alg/9502004OpenAlexW3099948578MaRDI QIDQ1910216

Terry Gannon

Publication date: 4 July 1996

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9502004

zbMATH Keywords

symmetriesclassification of conformal field theoriesaffine Coxeter Dynkin diagramKac-Peterson matricesnontwisted affine Kac-Moody algebra

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40)

Related Items (13)

Null-polygonal minimal surfaces in \(\mathrm{AdS}_{4}\) from perturbed \(W\) minimal models ⋮ Modular data: the algebraic combinatorics of conformal field theory ⋮ Automorphism modular invariants of current algebras ⋮ Unnamed Item ⋮ On the complete classification of unitary \(N = 2\) minimal superconformal field theories ⋮ \(U(1)^m\) modular invariants, \(N=2\) minimal models, and the quantum Hall effect ⋮ The \(W_N\) minimal model classification ⋮ Fixed points and fusion rings. Part 1 ⋮ \(g\)-functions and gluon scattering amplitudes at strong coupling ⋮ Boundary conformal field theory and fusion ring representations ⋮ Weight-lattice discretization of Weyl-orbit functions ⋮ The automorphisms of affine fusion rings. ⋮ Spectral measures for \(G_2\)

Cites Work

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• Non-Abelian bosonization in two dimensions
• 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
• Unitary representations of the Virasoro and super-Virasoro algebras
• The A-D-E classification of minimal and \(A_ 1^{(1)}\) conformal invariant theories
• Modular and conformal invariance constraints in representation theory of affine algebras
• Simple WZW currents
• Automorphisms of the affine \(SU(3)\) fusion rules
• The classification of affine \(SU(3)\) modular invariant partition functions
• Automorphism modular invariants of current algebras
• Implications of an arithmetical symmetry of the commutant for modular invariants.
• Simple Factors in the Jacobian of a Fermat Curve
• Towards a classification of su(2)⊕...⊕su(2) modular invariant partition functions
• Level one Kac-Moody characters and modular invariance

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