Root Systems


Quickref

  • T = CartanType(["A", 3]), T.is_finite() – Cartan types

  • T.dynkin_diagram(), DynkinDiagram(["G",2]) – Dynkin diagrams

  • T.cartan_matrix(),  CartanMatrix(["F",4]) – Cartan matrices

  • RootSystem(T).weight_lattice() – Root systems

  • WeylGroup(["B", 6, 1]).simple_reflections() – Affine Weyl groups

  • WeylCharacterRing(["D", 4]) – Weyl character rings

Introductory material

Cartan datum

Root systems

Coxeter groups

See also

The categories CoxeterGroups and WeylGroups

Finite reflection groups

See also

The category ComplexReflectionGroups

Representation theory

Root system data and code for specific families of Cartan types

Root system data and code for specific Cartan types