# GroupMath

 GroupMath 1.1.2 [6 May 2021; Current version] Fixes a problem which appears when using GroupMath in Mathematica 12.2 (Symbol a appears in multiple contexts). I thank Michael Ratz for pointing this out. GroupMath 1.1.1 [4 November 2020] Fixes the documentation files (gets rid of a distracting pop-up error message which may show up in version 1.1 whenever a help page is opened). GroupMath 1.1 [29 October 2020] A significant rewrite of the code (the symmetry breaking part in particular) was caried out. The function MaximalSubgroups now correctly identifies $SU(4) \times SU(4)$ as a maximal subgroup of $SU(16)$. Some functions were renamed: SubgroupEmbeddingCoefficients -> SubgroupCoefficients FindAllEmbeddings -> Embeddings PermutationSymmetryOfTensorParts -> PermutationSymmetry DrawYoungDiagram -> YoungDiagram CalculateSnBranchingRules -> SnBranchingRules This version of the program is described in the paper GroupMath: A Mathematica package for group theory calculations, arXiv:2011.01764 [hep-th]. GroupMath 1.0 [20 March 2020] Several improvements were made. The program now comes with a detailed built-in documentation. Several functions were added to the package, for example FindAllEmbeddings and MaximalSubgroups (please see the documentation for details). Improvements were made to some of the functions which already existed in earlier versions of GroupMath. It is now possible to use a simplified input format for representations of Lie groups (in many cases Dynkin coefficients are now unnecessary). For the representations with names $\boldsymbol{R}$ and $\overline{\boldsymbol{R}}$ (with no primes) it suffices to write R and -R, respectively. For example, previously the decomposition of $\boldsymbol{3}\times\boldsymbol{3}\times\overline{\boldsymbol{3}}$ in $SU(3)$ was calculated by writing ReduceRepProduct[SU3, {{1,0}, {1,0}, {0,1}}], but now it is also possible to do so with the code ReduceRepProduct[SU3, {3, 3, -3}]. GroupMath 0.11 [17 January 2019] Fixed a problem with folder paths which occurred while trying to load GroupMath on Linux (I thank Jorge Terol Calvo and Ricardo Cepedello for pointing this out). GroupMath 0.10 [28 August 2019] Fixed a problem in the Invariants function (I thank Andreas Trautner for pointing this out). GroupMath 0.9 [30 July 2019]