Représentations banales de
| Autor: | Alberto Mínguez, Vincent Sécherre |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Compositio Mathematica. 149:679-704 |
| ISSN: | 1570-5846 0010-437X |
| DOI: | 10.1112/s0010437x12000590 |
| Popis: | Let${\rm F}$be a non-Archimedean locally compact field of residue characteristic$p$, let${\rm D}$be a finite-dimensional central division${\rm F}$-algebra and let${\rm R}$be an algebraically closed field of characteristic different from$p$. We definebanalirreducible${\rm R}$-representations of the group${\rm G}={\rm GL}_{m}({\rm D})$. This notion involves a condition on the cuspidal support of the representation depending on the characteristic of${\rm R}$. When this characteristic is banal with respect to${\rm G}$, in particular when${\rm R}$is the field of complex numbers, any irreducible${\rm R}$-representation of${\rm G}$is banal. In this article, we give a classification of all banal irreducible${\rm R}$-representations of${\rm G}$in terms of certain multisegments, called banal. When${\rm R}$is the field of complex numbers, our method provides a new proof, entirely local, of Tadić’s classification of irreducible complex smooth representations of${\rm G}$. |
| Databáze: | OpenAIRE |
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