# Global square integrability ensures local sq. integrability?

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?

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I'm voting to close as "not a real question", hoping that the OP will clarify the context. – Andreas Blass Jan 4 '13 at 14:34
I think this is about as false as it's possible to be, isn't it? Any automorphic representation is unramified outside a finite set, and aren't unramified (local) representations essentially never square integrable? – user30035 Jan 4 '13 at 22:22
Andreas Blass: this is a question about representation theory of adelic algebraic groups, but I agree that it would have been much better if the OP had said this in any way other than by adding tags... – user30035 Jan 4 '13 at 22:23
Thanks wccanard. Then, is it true for ramified places? – Jude Jan 5 '13 at 3:59
A) At ramified places the local representation could be a ramified principal series, which will still not be square integrable, and it is, in general, difficult to say when this does or does not occur. B) A tempered automorphic representation is indeed one that is locally tempered everywhere. – B R Jan 5 '13 at 17:54