Coxeter-Dynkin diagram

After mathematicians H. S. M. Coxeter and Eugene Dynkin.

Coxeter-Dynkin diagram (plural Coxeter-Dynkin diagrams)

1. (geometry, algebra) A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

   A Coxeter-Dynkin diagram encodes the information in a Coxeter matrix, which in turn encodes the presentation of a Coxeter group.

   • 1995 June, R. V. Moody, J. Patera, Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices, Canadian Journal of Mathematics, page 597,

     Let 𝒬 be an indecomposable root lattice and let Γ denote the Coxeter-Dynkin diagram of the underlying root system Δ.

   • 2000, Andrei Gabrielov, Coxeter-Dynkin diagrams and singularities, Evgeniĭ Borisovich Dynkin, A. A. Yushkevich, Gary M. Seitz, A. L. Onishchik (editors), Selected Papers of E. B. Dynkin with Commentary, page 367,

     There is a deep and only partially understood connection between the classification and structure of singularities and the Coxeter-Dynkin diagrams introduced by H. S .M. Coxeter for classification of reflection-generated groups and by E. B. Dynkin for classification of semisimple Lie algebras.

   • 2012, Igor V. Dolgachev, Classical Algebraic Geometry: A Modern View‎, page 363:

     For 3 ≤ n ≤ 5, we will use E_n to denote the Coxeter-Dynkin diagrams of types A₁ + A₂(N = 3), A₄(N = 4) and D₅(N = 5).

• (graph with numerically labelled edges): Coxeter diagram, Coxeter graph

• Dynkin diagram