On representations of reductive p--adic groups over Q-algebras
| Autor: | Goran Muić |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Reduction (recursion theory) General Mathematics 010102 general mathematics reductive p-adic groups Q-admissible representations Hecke algebras Field (mathematics) Space (mathematics) 01 natural sciences Irreducible representation 0103 physical sciences 010307 mathematical physics 0101 mathematics Algebra over a field Mathematics::Representation Theory Representation (mathematics) Complex number Mathematics |
| DOI: | 10.3336/gm.55.2.04 |
| Popis: | In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some fundamental results in these settings, and as an example we give a classification of admissible unramified irreducible representations proving by reduction to the complex case that if the space of $K$--invariants is finite dimensional in an irreducible smooth unramified representation that the representation is admissible. |
| Databáze: | OpenAIRE |
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