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Local Converse Theorems for k-Middle Supercuspidal Representations of p-adic GL(kn)

  • Moshe Adrian
  • Michael Horzepa
  • David C. Luo
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Abstract

Let F be a non-archimedean local field of characteristic zero with residual characteristic p. In this paper, we study local converse theorems for k-middle supercuspidal representations of GL(kn, F) via explicit computations of twisted gamma factors on the Galois side, under the assumptions p nmid kn and qF>(k−1)2. Our results provide further evidence for a conjecture of the third-named author and Stevens on depth bounds for the twisting representations in the local converse theorem. For odd k ≥ 3, we obtain infinitely many families of supercuspidal representations for which the bound ⌊ kn/2 ⌋ in the local converse theorem is not sharp.

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Cite

BibTeXRIS
BibTeX
@misc{adrian2026local,
  title = {{Local Converse Theorems for $k$-Middle Supercuspidal Representations of $p$-adic $\textGL(kn)$}},
  author = {Moshe Adrian and Michael Horzepa and David C. Luo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24918},
  eprint = {2610.24918},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24918},
}
RIS
TY  - UNPB
TI  - Local Converse Theorems for k-Middle Supercuspidal Representations of p-adic GL(kn)
AU  - Moshe Adrian
AU  - Michael Horzepa
AU  - David C. Luo
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24918
UR  - https://arxiv.org/abs/2610.24918
AB  - Let F be a non-archimedean local field of characteristic zero with residual characteristic p. In this paper, we study local converse theorems for k-middle supercuspidal representations of GL(kn, F) via explicit computations of twisted gamma factors on the Galois side, under the assumptions p nmid kn and q_F>(k−1)^2. Our results provide further evidence for a conjecture of the third-named author and Stevens on depth bounds for the twisting representations in the local converse theorem. For odd k ≥ 3, we obtain infinitely many families of supercuspidal representations for which the bound ⌊ kn/2 ⌋ in the local converse theorem is not sharp.
ER  -