Unicity of types for supercuspidal representations of $ {\rm GL}_N$

• Autores: Vytautas Paskunas
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 91, Nº 3, 2005, págs. 623-654
• Idioma: inglés
• DOI: 10.1112/s0024611505015340
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let $F$ be a non-Archimedean local field, with the ring of integers $\mathfrak{o}_F$. Let $G = \mathrm{GL}_N(F)$, $K = \mathrm{GL}_N (\mathfrak{o}_F)$, and $\pi$ be a supercuspidal representation of $G$. We show that there exists a unique irreducible smooth representation $\tau$ of $K$, such that the restriction to $K$ of a smooth irreducible representation $\pi '$ of $G$ contains $\tau$ if and only if $\pi '$ is isomorphic to $\pi \otimes \chi \circ \det$, where $\chi$ is an unramified quasicharacter of $F^{\times}$. Moreover, we show that $\pi$ contains $\tau$ with the multiplicity 1. As a corollary we obtain a kind of inertial local Langlands correspondence.