A Julia library to compute D-functions, which are entries of the irreducible representations of the unitary group U(d). These entries can be numeric or symbolic.
Alternatively, you can install the package directly from the repository:
user@machine:~$ mkdir new_code && cd new_code
user@machine:~$ julia --project=.
julia> ] add https://github.com/davidamaro/GroupFunctions.jl- Mac: Use
juliaup. Installing Julia viabrewis not recommended. - Linux: Use the appropriate package manager (e.g.,
sudo pacman -S julia). - Windows: Run
winget install julia -s msstorein your terminal and follow the steps.
julia> using RandomMatrices # You may be asked to install it. Just answer yes.
julia> using GroupFunctions
julia> my_fav_irrep = [2, 1, 0]
julia> my_fav_matrix = rand(Haar(2), 3)
julia> my_fav_basis = basis_states(my_fav_irrep)
julia> # Check out some cool Gelfand-Tsetlin patterns:
julia> my_fav_basis[1]
julia> my_fav_basis[3]
julia> group_function(my_fav_irrep, my_fav_basis[1], my_fav_basis[3], my_fav_matrix)
julia> # For a symbolic matrix, simply omit the matrix argument
julia> output = group_function(my_fav_irrep, my_fav_basis[1], my_fav_basis[3])
julia> # Translate the symbolic D-function for use in Mathematica
julia> julia_to_mma(output)For more examples, see the "Tutorials" section in the documentation.
Contributions are welcome! Please feel free to submit a Pull Request. A to-do list is included in the todo.txt file.
Until the code from AbstractAlgebra.jl (to deal with Young tableaux) is removed from this package, the license will align with AbstractAlgebra.jl's.
- J Grabmeier and A Kerber, "The evaluation of irreducible polynomial representations of the general linear groups and of the unitary groups over fields of characteristic 0" Acta Appl. Math, 1987
- A Alex et al, "A numerical algorithm for the explicit calculation of SU(N) and SL(N, C) Clebsch–Gordan coefficients" J. Math. Phys. 2011
- D Amaro-Alcala et al "Sum rules in multiphoton coincidence rates" Phys. Lett. A 2020
- AbstractAlgebra.jl
Pending.
