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November 4, 2026Open Access

Non-admissible smooth irreducible representations of GL₂(F) for totally ramified extensions F/Qₚ

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Abstract

Let p≥ 5, and let F/Qₚ be a nontrivial finite totally ramified extension. We construct a non-admissible smooth irreducible representation of GL₂(F) over F̄ₚ. The construction uses representations of GL₂(OF) on which the first principal congruence subgroup acts nontrivially, together with a deformation of a diagram indexed by Z.

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Cite This Study

Dayu Huang (2026) studied this question.

synapsesocial.com/papers/6aeec02e2765dd7d89fe55c6 https://doi.org/10.48550/arxiv.2611.06056

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