This question already has an answer here:
In a question answered on this site concerning how group theory worked its way into quantum mechanics it was proposed that this was done by Weyl while investigating the many electron problem. Yes, but how then did a problem concerning many electrons by use of groups and symmetry permutations end up with formulations of Lie groups predicting the existence of the very particles that were assumed to exist from the many electron problem. This fanciful idea again worked its way into the Standard Model to predict quarks using the "eightfold" way. And to mystify this even more the essence of the unification of the particles is actually seen when the very symmetry used to predict the particles is broken. Very puzzling. Any historical maps of how symmetry flows through the Standard Model is welcome.