GroupFunctions.jl manual

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Description

GroupFunctions started as an extension for AbstractAlgebra.jl but some time later I found out that it was quite different. This is an unregistered Julia package.

Features

The features of GroupFunctions.jl include:

  • Computing group function for $\mathrm{U}(n)$
  • Generate GT patterns
  • Generate Semi Standard Young Tableaux (based on AbstractAlgebra.jl)
  • Compute Orthogonal/Yamanouchi irreducible representations (irrep)

Installation

In Julia's blue prompt (accesed by pressing ])

add https://github.com/davidamaro/GroupFunctions.jl

Computing group functions

GroupFunctions.group_functionFunction
group_function(λ::Irrep, tu::YTableau, tv::YTableau)

Return the symbolic group function corresponding to irrep λ and semistandard Young Tableaux (STYT) tu and tv.

Example:

julia> t = YoungTableau([2,1]); fill!(t, [1,2,3]);
julia> group_function([2,1,0], t, t)
source
group_function(λ::Irrep, tu::GTPattern, tv::GTPattern)

Return the symbolic group function corresponding to irrep λ and GT patterns tu and tv.

Example:

julia> t = GTPattern([[2,1,0],[2,1],[2]],[2]);
julia> group_function([2,1,0], t, t)
source
group_function(λ::Irrep, tu::GTPattern, tv::GTPattern, mat::Array{Complex{Float64},2})

Return the numeric group function, for an SU(n) member mat, corresponding to irrep λ and a pair of GT patterns tu and tv.

julia> using RandomMatrices
julia> mat = rand(Haar(2),3)
julia> t = GTPattern([[2,1,0],[2,1],[2]],[2]);
julia> group_function([2,1,0], t, t, mat)
source
group_function(λ::Irrep, tu::GTPattern, tv::GTPattern, mat::Array{Complex{Float64},2})

Return the numeric group function, for an SU(n) member mat, corresponding to irrep λ and STYT tu and tv.

Example:

julia> using RandomMatrices
julia> mat = rand(Haar(2),3)
julia> t = YoungTableau([2,1]); fill!(t, [1,2,3]);
julia> group_function([2,1,0], t, t, mat)
source

Note that the recommended input structure is GTPattern as being easier to obtain more info on the state that it labels.