Documentation

group_function(λ::Irrep, tu::YoungTableau, tv::YoungTableau)

Returns the symbolic group function corresponding to irrep λ and Young tableaux tu and tv.

Example:

julia> t = YoungTableau([2,1]); fill!(t, [1,2,3]);
julia> group_function([2,1,0], t, t)

group_function(λ::Irrep, tab_u::YTableau, tab_v::YTableau; verbose::Bool = false) -> Basic

Compute group theoretical function based on Young tableaux and irreducible representations.

Arguments:

• λ::Irrep: Irreducible representation
• tab_u::YTableau: First Young tableau
• tab_v::YTableau: Second Young tableau
• verbose::Bool: Flag for detailed output (default: false)

Returns:

• Complex: Group function evaluated

Notes:

• Uses SymEngine for symbolic computation
• Involves matrix operations and coset calculations

group_function(λ::Irrep, tu::GTPattern, tv::GTPattern)

Returns 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)

group_function(λ::Irrep, pat_u::GTPattern, pat_v::GTPattern; verbose::Bool = false) -> Basic

Compute group theoretical function based on Gelfand-Tsetlin patterns and irreducible representations.

Arguments:

• λ::Irrep: Irreducible representation
• pat_u::GTPattern: First Gelfand-Tsetlin pattern
• pat_v::GTPattern: Second Gelfand-Tsetlin pattern
• verbose::Bool: Flag for detailed output (default: false)

Returns:

• Basic: Computed polynomial expression in SymEngine format

Notes:

• Converts GT patterns to Young tableaux for calculations
• Uses SymEngine for symbolic computation

group_function(λ::Irrep, tu::GTPattern, tv::GTPattern, mat::Array{Complex{Float64},2})

Returns 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)

group_function(λ::Irrep, tu::GTPattern, tv::GTPattern, mat::Array{Complex{Float64},2})

Returns 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)

GTPattern(arrayofarrays)

Example:

julia> GTPattern([[2,1,0],[2,1],[2]])
│ 2 1 0 ╲
│ 2 1    〉
│ 2     ╱

bloquesun(size::Int64, position::Int64, angles::Tuple{Float64,Float64,Float64})

Computes the SU(2) matrix using angles an embeds it into a size times size matrix.

Example:

α5,β5 = rand(Float64,2)
yy2=bloquesun(4,2,(α5,β5,α5))