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 for $SO(n)$ or $SU(n)$, in various basis. Specifically, I'm looking for the $SO(10)$ generators in the standard basis and the Cartan-Weyl basis.

Does such a package exist somewhere?

  • $\begingroup$ Once you have explicit generators, split is not a problem, because you always can use trace formula (1/d) Tr(A B) to ,,project'' given matrix A onto the generator B (d being matrix dimension). For larger groups, however, generators can be chosen in many ways. $\endgroup$ – user18792 Aug 5 '15 at 15:58

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