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PreprintarXiv licencearXiv

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

  • Dayu Huang
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Abstract

Let pā‰„ 5, and let F/ā„šp be a nontrivial finite totally ramified extension. We construct a non-admissible smooth irreducible representation of GL2(F) over š”½Ģ…p. The construction uses representations of GL2(š’ŖF) on which the first principal congruence subgroup acts nontrivially, together with a deformation of a diagram indexed by ā„¤.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026nonadmissible,
  title = {{Non-admissible smooth irreducible representations of $\mathrmGL_2(F)$ for totally ramified extensions $F/\mathbbQ_p$}},
  author = {Dayu Huang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06056},
  eprint = {2611.06056},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06056},
}
RIS
TY  - UNPB
TI  - Non-admissible smooth irreducible representations of GL_2(F) for totally ramified extensions F/ā„š_p
AU  - Dayu Huang
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06056
UR  - https://arxiv.org/abs/2611.06056
AB  - Let pā‰„ 5, and let F/ā„š_p be a nontrivial finite totally ramified extension. We construct a non-admissible smooth irreducible representation of GL_2(F) over š”½Ģ…_p. The construction uses representations of GL_2(š’Ŗ_F) on which the first principal congruence subgroup acts nontrivially, together with a deformation of a diagram indexed by ā„¤.
ER  -