very simple question on SM

[Neitrino]

Dear All,
I dont understand how/why Halzen Martin use J_em J_3 and introduced J_Y currents to build SU(2)*U(1) theory....can anyone advise something...

thank you

[Angryphysicist]

I would suspect perhaps because these are the Casimir operators of the group? Just a wild guess, I don't have a copy of Halzen Martin's book or work or am I able to find a relevant quote :(