Replication code for the manuscript "Efficient construction and explicit dimensionality of Lie group-equivariant and permutation-invariant spaces"
Year: 2026
Type: software
Abstract: This repository contains the source code and scripts used to generate all results and figures reported in the manuscript: Eloïse Barthelemy, Geneviève Dusson, Camille Hernandez, and Liwei Zhang, "Efficient construction and explicit dimensionality of Lie group-equivariant and permutation-invariant spaces", arxiv.2604.01975, 2026. Contents - `constructing_GE-PI_basis_via_lie_alg.jl` — Implementation of the proposed method on SO3 - Julia code. - `constructing_GE-PI_basis_via_lie_alg_SU2.jl` — Implementation of the proposed method on SU2 - Julia code. - `recursive_construction.jl` - Implementation of the proposed recursive method on SO3 - Julia code. - `dim_utils.jl` — Code for computing dimensions - Julia code. - `cache_dim.jld2` - JLD2 file containing cached dimensionalities to avoid duplicate computations. - `script_plots.jl` — Scripts generating figures shown in the manuscript - Julia code. - `cost_plots.jl` — Part of `script_plots.jl`, containing codes for generating the cost figures shown in the manuscript - Julia code. - `recursive_plots.jl` — Part of `script_plots.jl`, containing codes for generating figures regarding the comparison of recursive and direct constructions shown in the manuscript - Julia code. - `code_for_effciency_comparison/` — Folder of scripts running the benchmark of the proposed method and existing methods - Julia and Python codes. - `Project.toml`, `Manifest.toml` — Exact Julia environment for reproducibility. Requirements - Julia ≥ 1.10 - Python ≥ 3.8
Institutions: Université Marie et Louis Pasteur, RWTH Aachen University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223745281