GroupMath: A Mathematica package for group theory calculations

GroupMath is a Mathematica package which performs several calculations related to semi-simple Lie algebras and the permutation groups, both of which are important in various areas of physics. Having in mind the specific needs of theoretical particle physicists, the program computes several basis-independent quantities (such as roots, weights, decomposition of products of representations, branching rules) as well as basis-dependent ones (including explicit representation matrices and Clebsch-Gordon coefficients).

GroupMath是一款Mathematica软件包，旨在执行与半简单李代数及排列群相关的多种计算。此类代数和群在物理学的多个领域扮演着至关重要的角色。考虑到理论粒子物理学家的特定需求，该程序能够计算多种与基无关的量（例如根、权重、表示乘积的分解、分支规则）以及与基相关的量（包括显式的表示矩阵和克莱布斯-戈登系数）。