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SUMMARY:Automorphic representations of prescribed type - Sug Woo Shin (Chi
 cago)
DTSTART:20091013T133000Z
DTEND:20091013T143000Z
UID:TALK19859@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:Let _G_ be a connected reductive group over a number field _F_
 . Let _S_ be a finite set of places of _F_. Assuming certain facts in repr
 esentation theory including the local Langlands classification\, we will e
 xplain how the simple trace formula (together with the stable trace formul
 a formalism) allows us to find an automorphic representation of _G_(*A*__F
 _) which has prescribed _types_ on _S_. In fact we prove that there are _m
 any_ representations of any prescribed type. (This kind of result may be w
 ell-known to experts in the trace formula.) If we restrict to the case of 
 discrete series types\, the result is unconditional due to Clozel (1980's)
 . If _G_ is an inner form of a product of general linear groups on _S_\, t
 he result is also unconditional. If time permits\, we interpret this in te
 rms of Galois representations.
LOCATION:MR13
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