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Title of Journal: Invent math

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Abbravation: Inventiones mathematicae

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Springer-Verlag

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10.1002/zaac.19492590509

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1432-1297

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The classification of irreducible admissible mod

Authors: Florian Herzig
Publish Date: 2011/03/18
Volume: 186, Issue: 2, Pages: 373-434
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Abstract

Let F be a finite extension of ℚ p Using the mod p Satake transform we define what it means for an irreducible admissible smooth representation of an Fsplit padic reductive group over overline mathbbF p to be supersingular We then give the classification of irreducible admissible smooth GL n Frepresentations over overline mathbbF p in terms of supersingular representations As a consequence we deduce that supersingular is the same as supercuspidal These results generalise the work of Barthel–Livné for n=2 For general split reductive groups we obtain similar results under stronger hypotheses


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