This might be a stupid question for expert in this area.

I am considering automorphic representation of algebraic group.

In studying it, local tempered, local square integrable representations occurs in the P-adic group case. So, I am wondering that what global automorphic representation gives rise to such representation at some finite set of places?

Does globally sq. int. auto. represenation give local sq. int reps at S, some finite set of places of F?

If not, would you tell me what kind of global automorphic representation would be locally sq. int for finite set of places?

One more notation question.

What is the meaning of tempered auto. reps. in global situation? For I learned its definition only in the local case, I suppose it should be locally tempered at finite ramified places. Is it ture?