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

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 F-split p-adic reductive group over \bar F_p to be supersingular. We then give the classification of irreducible admissible smooth GL_n(F)-representations over \bar 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-Livne for n = 2. For general split reductive groups we obtain similar results under stronger hypotheses.

55 pages, to appear in Inventiones Mathematicae

References in corpus (2)

• A Satake isomorphism in characteristic p
• On special representations of $p$-adic reductive groups

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