The spectrum of a Coxeter transformation, affine Coxeter transformations, and the defect map

DOI10.1016/0021-8693(89)90070-7zbMath0679.17007OpenAlexW2031954991MaRDI QIDQ1822600

Yanyan Li

Publication date: 1989

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90070-7

zbMATH Keywords

Cartan matrixWeyl groupeigenvaluesCoxeter transformationdefect mapaffine Cartan matrix

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (19)

On spectral radii of Coxeter transformations. ⋮ The spectral radius of the Coxeter transformations for a generalized Cartan matrix ⋮ Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case ⋮ A'Campo's theorem on the discriminant ⋮ On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number ⋮ Quantum affine Cartan matrices, Poincaré series of binary polyhedral groups, and reflection representations. ⋮ The action of a Coxeter element on an affine root system ⋮ Poincaré series for tensor invariants and the McKay correspondence ⋮ The enumeration of Coxeter elements ⋮ On the periodicity of Coxeter transformations and the non-negativity of their Euler forms ⋮ Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case ⋮ Coxeter transformations: construction of deltoids ⋮ Aspects of affine Toda field theory ⋮ Conjugacy relation on Coxeter elements ⋮ Poincaré series, exponents of affine Lie algebras, and McKay-Slodowy correspondence ⋮ On \(A_1^2\) restrictions of Weyl arrangements ⋮ Killing and the Coxeter transformation of Kac-Moody algebras ⋮ Eigenvalues of coxeter transformations and the structure of regular componentsof an auslander-reiten quiver ⋮ The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory

Cites Work

• Infinite dimensional Lie algebras. An introduction
• Finite subgroups of \(SU_ 2\), Dynkin diagrams and affine Coxeter elements
• Sur les valeurs propres de la transformation de Coxeter
• Affine root systems and Dedekind's \(\eta\)-function
• The product of the generators of a finite group generated by reflections
• On finite subgroups of SU(2), simple Lie algebras, and the McKay correspondence
• Coxeter Groups and M -Matrices
• Eigenvalues of Coxeter Transformations and the Gelfand-Kirillov Dimension of the Preprojective Algebras
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