PreprintCC BY 4.0arXiv
GroupFunctions.jl: computing individual entries of the irreducible representations of the unitary group U(d)
Abstract
GroupFunctions.jl is a Julia library for computing individual matrix elements of irreducible representations of U(d). These matrix elements, called group functions, can be evaluated symbolically or numerically. For SU(2), they reduce to the Wigner D-functions. The library computes these matrix elements in a carrier-space basis enumerated by Gelfand-Tsetlin patterns. It can also compute entire representation operators, construct input unitaries from parameterisations common in quantum optics, translate Gelfand-Tsetlin patterns into occupation-number kets, and compute the associated Schur functions. Results can be exported in a form compatible with Mathematica.
Versions
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BibTeX
@misc{amaroalcala2026groupfunctionsjl,
title = {{GroupFunctions.jl: computing individual entries of the irreducible representations of the unitary group U(d)}},
author = {David Amaro-Alcalá and Konrad Szymański},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.10867},
eprint = {2607.10867},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10867},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GroupFunctions.jl: computing individual entries of the irreducible representations of the unitary group U(d)
AU - David Amaro-Alcalá
AU - Konrad Szymański
PY - 2026
DA - 2026/07/12
PB - arXiv
DO - 10.48550/arxiv.2607.10867
UR - https://arxiv.org/abs/2607.10867
AB - GroupFunctions.jl is a Julia library for computing individual matrix elements of irreducible representations of U(d). These matrix elements, called group functions, can be evaluated symbolically or numerically. For SU(2), they reduce to the Wigner D-functions. The library computes these matrix elements in a carrier-space basis enumerated by Gelfand-Tsetlin patterns. It can also compute entire representation operators, construct input unitaries from parameterisations common in quantum optics, translate Gelfand-Tsetlin patterns into occupation-number kets, and compute the associated Schur functions. Results can be exported in a form compatible with Mathematica.
ER -