On the existence of nonadmissible irreducible smooth representations of $p$-adic $\mathrm{GL}_n$

arXiv:2611.05552v1 Announce Type: new Abstract: Let $p>7$ be a prime, let $n>1$, and let $F$ be a nonarchimedean local field of residue characteristic $p$ not equal to $\mathbb{Q}_p$. For every extension $E$ of the residue field of $F$, we construct an irreducible smooth $E$-representation of $\mathrm{GL}_n(F)$ which is not admissible. When $E$ is countable, we also construct such representations without a central character and with nonscalar endomorphisms.

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