2020/07/05 by Kaashif Hymabaccus, Hymabaccus, Kaashif, Dmitrii V. Ṗasechnik +2
Computer Science · Engineering · Mathematics · #20C99 #Algebra over a field #Coding theory and cryptography #Computer science #Decomposition #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Mathematics #Open source #Parallel computing #Programming language #Pure mathematics #Representation (politics) #Representation Theory (math.RT) #Ring (chemistry) #Software #Theoretical computer science #Zero (linguistics) #graph theory and CDMA systems #math.GR #math.RT #msc:20C99
paper · pdf · doi:10.48550/arxiv.2007.02459
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2020/07/05 · arxiv created 2020/07/08 · arxiv updated 2020/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We develop a package using the computer algebra system GAP for computing the decomposition of a representation ρ of a finite group G over ℂ into irreducibles, as well as the corresponding decomposition of the centraliser ring of ρ(G). Currently, the only open-source programs for decomposing representations are for non-zero characteristic fields. While methods for characteristic zero are known, there are no open-source computer programs that implement these methods, nor are details on how to achieve good performance of such an implementation published. We aim to record such details and demonstrate an application of our program in reducing the size of semidefinite programs.