Let F be a finite extension of ?_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over F?_p to be supersingular. We then give the classification of irreducible admissible smooth GL_n(F)-representations over F?_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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机译：令F为？_p的有限扩展。使用mod p Satake变换，我们定义了F？_p上的F分裂p-adic还原基团的不可约的容许光滑表示是超奇数意味着什么。然后，根据超奇异表示，对F？_p给出不可约的容许光滑GL_n（F）表示的分类。结果，我们推论超奇与尖峰相同。这些结果推广了Barthel-Livné在n = 2时的工作。对于一般的分裂归约组，我们在更强的假设下获得了相似的结果。
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