Irreducible decomposition

DecomposingGroupRepresentations.IrreducibleDecomposition — Type

IrreducibleDecomposition

Represents a decomposition of a group representation into a collection of irreducible representations.

Constructors

IrreducibleDecomposition(ρ::GroupRepresentation)

Examples

julia> @polyvar x y z;

julia> vars = [x, y, z];

julia> SO3 = LieGroup("SO", 3);

julia> a = MatrixGroupAction(SO3, [vars]);

julia> V = FixedDegreePolynomials(vars, 2);

julia> ρ = GroupRepresentation(a, V);

julia> irreducibles(ρ)
IrreducibleDecomposition of SO(3)-action on 6-dimensional vector space
 number of irreducibles: 2
 dimensions of irreducibles: 1, 5

source

DecomposingGroupRepresentations.irreducibles — Method

irreducibles(::AbstractGroupRepresentation) -> IrreducibleDecomposition

Returns a decomposition into irreducible subrepresentations of the given group representation.

source