Isotypic decomposition

DecomposingGroupRepresentations.IsotypicDecomposition — Type
IsotypicDecomposition

Represents the isotypic decomposition of a group representation.

Constructors

IsotypicDecomposition(ρ::GroupRepresentation)

Examples

julia> @polyvar x[1:3] y[1:3];

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

julia> a₁ = MatrixGroupAction(SO3, [x, y]);

julia> a₂ = ScalingLieGroupAction(vcat(x, y));

julia> a = a₁ × a₂;

julia> V = FixedDegreePolynomials(vcat(x, y), 2);

julia> ρ = GroupRepresentation(a, V)
GroupRepresentation of SO(3) × ℂˣ on 21-dimensional vector space
 Lie group: SO(3) × ℂˣ

julia> isotypics(ρ)
IsotypicDecomposition of SO(3) × ℂˣ-action on 21-dimensional vector space
 number of isotypic components: 3
 multiplicities of irreducibles: 3, 3, 1
 dimensions of irreducibles: 1, 5, 3
 dimensions of isotypic components: 3, 15, 3
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