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是一款可执行多项与半单李代数（semi-simple Lie algebras）及置换群（permutation groups）相关计算的Mathematica软件包，这两类对象在诸多物理学领域中均具有重要意义。考虑到理论粒子物理学家的特定需求，该程序可计算多项与基无关的物理量（如根、权、表示乘积的分解、分支规则等），同时也可计算与基相关的物理量，包括显式表示矩阵与克莱布希-戈登系数（Clebsch-Gordon coefficients）。