DecomposingGroupRepresentations.jl

DecomposingGroupRepresentations.jl is a Julia package for decomposing representations of reductive groups acting on multivariate polynomials.

Installation

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add DecomposingGroupRepresentations

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Usage

using DecomposingGroupRepresentations

@polyvar x y z
vars = [x, y, z]
SO3 = LieGroup("SO", 3)
a = MatrixGroupAction(SO3, [vars])
V = FixedDegreePolynomials(vars, 2)
ρ = GroupRepresentation(a, V)

irreducibles(ρ)

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