Understanding Halzen Martin's Use of J_em and J_Y in SU(2)*U(1) Theory

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Neitrino
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Dear All,
I don't 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
 
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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 :(
 

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