Classifying quarks and leptons using LCTs

[Investion]

Hi everyone, I would like to ask for opinions/expertises on the relations between quarks, leptons and spin representation of linear canonical transformations (LCTs) as described in this link 

https://en.wikipedia.org/wiki/Linear_canonical_transformation#Relation_to_particle_physics

Please find below a picture describing this relation as taken from the link. My main questions are  : 

1- Are the statements in this link correct and compatible with mainstream particle physics ? (any contradiction?)

2-Could someone explain with more details how to deduce this classification? (if it is correct ?) 

 

Thank you in advance