Timeline for How badly can strong multiplicity one fail in the theory of automorphic representations?
Current License: CC BY-SA 3.0
6 events
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| Sep 6, 2011 at 18:52 | comment | added | Kevin Buzzard | Aah yes of course Matt -- (3) is obviously false in general because it fails already for $GL(2)$. | |
| Sep 6, 2011 at 18:52 | history | edited | anonymous | CC BY-SA 3.0 |
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| Sep 6, 2011 at 18:31 | comment | added | Emerton | Just to reiterate Kevin's question from his first comment: Are you restricting to some particular $\pi$s here? For example, already in the case of $GL_2$, in the non-cuspidal spectrum we have reps. which are nearly equivalent but not isomorphic (as Kevin notes), and the A-packets are singletons in this case. E.g. are you restricting to automorphic reps. in the L^2-spectrum? Regards, Matthew | |
| Sep 6, 2011 at 18:23 | comment | added | Kevin Buzzard | PS I own A-B-V. Can you be more precise about a reference? Or give an explicit $G$ for which (1) and (3) should fail? Is $PGSp(4)$ a good candidate? | |
| Sep 6, 2011 at 18:21 | comment | added | Kevin Buzzard | I thought that Arthur packets somehow didn't cover all representations and one had to put some sort of restriction on the automorphic representations one considered. Let me say that I know zilch about A-packets. Do I have to restrict to some subset of $\pi$s before A-packet stuff applies? | |
| Sep 6, 2011 at 18:14 | history | answered | anonymous | CC BY-SA 3.0 |