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#