Association schemes and fusion algebras. (An introduction)

DOI10.1023/A:1022489416433zbMath0790.05098MaRDI QIDQ1310597

Eiichi Bannai

Publication date: 22 June 1994

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

character algebraassociation schemefusion algebrasmodular invariance

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Association schemes, strongly regular graphs (05E30) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Finite commutative rings (13M99)

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Spin models on finite cyclic groups, (𝑛+1,𝑚+1)-hypergeometric functions associated to character algebras, Modular data: the algebraic combinatorics of conformal field theory, On spin models, modular invariance, and duality, Modular invariance property and spin models attached to cyclic group association schemes, Classification of super-modular categories by rank, Construction of rank 4 self‐dual association schemes inducing three partial geometric designs, Character groups of dihedral and generalized quaternion groups, Subfactors from graphs induced by association schemes, Optimal line packings from nonabelian groups, Algebras Associated to the Young-Fibonacci Lattice, Augmented quasigroups and character algebras, On spin models, triply regular association schemes, and duality, Circulant association schemes on triples, Spin models and Bose-Mesner algebras, Bose-Mesner algebras related to type II matrices and spin models, Commutative association schemes, Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey), Transposable character tables and group duality

Cites Work

• Fusion rules and modular transformations in 2D conformal field theory
• Classical and quantum conformal field theory
• The operator algebra of orbifold models
• Modular invariance of the character table of the Hamming association scheme \(H(d,q)\)
• Modular invariance and the fusion algebra
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