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On the existence of nonadmissible irreducible smooth representations of p-adic GLn
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 ℚp. For every extension E of the residue field of F, we construct an irreducible smooth E-representation of GLn(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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BibTeX
@misc{le2026existence,
title = {{On the existence of nonadmissible irreducible smooth representations of $p$-adic $\mathrmGL_n$}},
author = {Daniel Le and Mansimar Singh},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05552},
eprint = {2611.05552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05552},
}
RIS
TY - UNPB
TI - On the existence of nonadmissible irreducible smooth representations of p-adic GL_n
AU - Daniel Le
AU - Mansimar Singh
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05552
UR - https://arxiv.org/abs/2611.05552
AB - Let p>7 be a prime, let n>1, and let F be a nonarchimedean local field of residue characteristic p not equal to ℚ_p. For every extension E of the residue field of F, we construct an irreducible smooth E-representation of GL_n(F) which is not admissible. When E is countable, we also construct such representations without a central character and with nonscalar endomorphisms.
ER -