Automorphic representations of prescribed type

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• Sug Woo Shin (Chicago)
• Tuesday 13 October 2009, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Tom Fisher.

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 representation theory including the local Langlands classification, we will explain how the simple trace formula (together with the stable trace formula 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 many representations of any prescribed type. (This kind of result may be well-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, the result is also unconditional. If time permits, we interpret this in terms of Galois representations.

This talk is part of the Number Theory Seminar series.

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