The classification of irreducible admissible mod p representations of a p-adic GL n
| Autor: | Florian Herzig |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Overline Mathematics - Number Theory Mathematics::Number Theory General Mathematics 010102 general mathematics Extension (predicate logic) Reductive group 01 natural sciences Mathematics::Algebraic Geometry Mod 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Representation (mathematics) Mathematics - Representation Theory Mathematics |
| Zdroj: | Inventiones mathematicae. 186:373-434 |
| ISSN: | 1432-1297 0020-9910 |
| DOI: | 10.1007/s00222-011-0321-z |
| Popis: | 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. Comment: 55 pages, to appear in Inventiones Mathematicae |
| Databáze: | OpenAIRE |
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