Representations of a reductive $p$-adic group in characteristic distinct from $p$
| Autor: | Guy Henniart, Marie-France Vignéras |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Popis: | We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over a field $C$ of characteristic different from $p$. When $C$ is algebraically closed, for many groups $G$, a list of cuspidal $C$-types $(J,\lambda)$ has been produced satisfying exhaustion, sometimes for a restricted kind of cuspidal representations, and often unicity. We verify that those lists verify Aut($C$)-stability and we produce similar lists when $C$ is no longer assumed algebraically closed. Our other main results concern supercuspidality. This notion makes sense for the representations $\lambda$ in the cuspidal $C$-types $(J,\lambda)$ as above, which involve finite reductive groups. We check that an irreducible cuspidal representation of $G$ induced from $\lambda$ is supercuspidal if and only $\lambda$ is supercuspidal. Comment: 45 pages This is the final version |
| Databáze: | OpenAIRE |
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