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arXiv · 2611.06056

Non-admissible smooth irreducible representations of $\mathrm{GL}_2(F)$ for totally ramified extensions $F/\mathbb{Q}_p$

Dayu Huang
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Abstract

Let $p\geq 5$, and let $F/\mathbb{Q}_p$ be a nontrivial finite totally ramified extension. We construct a non-admissible smooth irreducible representation of $\mathrm{GL}_2(F)$ over $\overline{\mathbb{F}}_p$. The construction uses representations of $\mathrm{GL}_2(\mathcal{O}_F)$ on which the first principal congruence subgroup acts nontrivially, together with a deformation of a diagram indexed by $\mathbb{Z}$.

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Dayu Huang. 2026-11-04. Non-admissible smooth irreducible representations of $\mathrm{GL}_2(F)$ for totally ramified extensions $F/\mathbb{Q}_p$. https://arxiv.org/abs/2611.06056

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