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¶

Root Systems – This overview
CartanType – An introduction to Cartan types
RootSystem – An introduction to root systems
Tutorial: visualizing root systems – A root system visualization tutorial
The Lie Methods and Related Combinatorics thematic tutorial

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¶