Inventiones mathematicae

, Volume 186, Issue 2, pp 373–434

The classification of irreducible admissible mod p representations of a p-adic GLn


DOI: 10.1007/s00222-011-0321-z

Cite this article as:
Herzig, F. Invent. math. (2011) 186: 373. doi:10.1007/s00222-011-0321-z


Let F be a finite extension of ℚp. 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 \(\overline{ \mathbb{F}}_{p}\) to be supersingular. We then give the classification of irreducible admissible smooth GLn(F)-representations over \(\overline{ \mathbb{F}}_{p}\) 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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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsEvanstonUSA