The classification of irreducible admissible mod p representations of a p-adic GLn
By F. Herzig. 2010
105 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9b5dbc6f7388d4bc8858c886de082b3b2aa772c2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Parabolic induction and Hecke modules in characteristic p for p-adic GLn (2010, background): “A barrier to further investigation of the pro-p-invariant subspace of the irreducible induced representations classified in [Herzig 2010] is the lack of knowledge of the (pro-p-invariants of) supersingular representations of L , for general L and F .”
- Towards a Modulo p Langlands Correspondence for GL2 (2012, background): “Note that the non-supersingular representations of GLn(F ) over Fp are now well understood thanks to [20] up to understanding the supersingular representations of GLm(F ) for m < n.”
- The emerging p-adic Langlands programme (2011, background): “For GLn(Qp) when n > 2 the modulo p Langlands programme is essentially open (although there is recent progress in the classification of “non-supersingular” smooth irreducible admissible representations of GLn(F ) over kE , see [40]).”