Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$

Eknath Ghate; Daniel Le; Mihir Sheth

doi:10.1090/ert/660

Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$

Representation Theory 2025-10-28 v4 Number Theory

Authors: Eknath Ghate , Daniel Le , Mihir Sheth

View on arXiv ↗ PDF ↗ DOI ↗

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

Keywords

p-adic gl_n non-admissible representations irreducible representations breuil-paskunas diagrams parabolic induction local field

Cite

@article{arxiv.2210.07281,
  title  = {Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$},
  author = {Eknath Ghate and Daniel Le and Mihir Sheth},
  journal= {arXiv preprint arXiv:2210.07281},
  year   = {2025}
}

Comments

15 pages, this version contains the erratum to the published version: the permutation $g$, the statement of Prop 3.1 and its proof, and the proof of Thm 1.2 are corrected

Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$

Abstract

Keywords

Cite

Comments

Related papers