Non-admissible irreducible representations of $p$-adic ${\mathrm{GL}}_n$ in characteristic $p$

Abstract

Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of ${\mathbb{F}}_p$. We construct smooth absolutely irreducible non-admissible representations of ${\mathrm{GL}}_2(F)$ defined over the residue field of $F$ extending the earlier results of the authors for $F$ unramified over ${\mathbb{Q}}_p$. This construction uses the theory of diagrams of Breuil and Paskunas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of ${\mathrm{GL}}_n(F)$ for $n>2$.

15 pages, this version contains the erratum to the published version: the permutation $g$, the statement of Prop 3.1 and its proof, and the proof of Thm 1.2 are corrected

References in corpus (1)

• On irreducible supersingular representations of ${\mathrm{GL}}_2(F)$