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

Ghate, Eknath; Le, Daniel; Sheth, Mihir

doi:10.1090/ert/660

Non-admissible irreducible representations of $p$-adic $\mathrm {GL}_{n}$ in characteristic $p$
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by Eknath Ghate, Daniel Le and Mihir Sheth;

Represent. Theory 27 (2023), 1088-1101

DOI: https://doi.org/10.1090/ert/660

Published electronically: November 6, 2023

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

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