While there are several packages that are capable of working with weights and roots (for example LieArt), I couldn't find any package that spits out explicit matrices for the generators, for example ...
I have a (large, finite, permutation) group, and a group element that I know is a product of length=20 of the generators. But when I ConvertGroupElementToWord, I get a word of length=118. Other, ...
I want to find a function like FiniteGroupData but for finite rings. Does something like that exists?
Apparently, it is possible to do Young Tableaux calculations with mathematica (see the Susyno and LieART packages). A natural follow up question is then, given that one has decomposed a direct product ...