Non-admissible irreducible representations of 𝑝-adic 𝐺𝐿_{𝑛} in characteristic 𝑝

Abstract

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