Non-admissible irreducible representations of p-adic \mathrm{GL}_{n} in characteristic p.

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 Pašk\bar {\mathrm {u}}nas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of \mathrm {GL}_n(F) for n>2. [ABSTRACT FROM AUTHOR]