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PreprintarXiv licencearXiv

Bounds for (k,c) model functions over p-adic fields

  • Eyal Kaplan
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Abstract

Let F be a p-adic field, let k,c≥1, and let ρ be a (k,c) representation of GLkc(F): a complex representation of finite length whose wave front set has (kc) as its unique maximal orbit, and which admits a (k,c) functional that is unique up to scaling. We prove that the functions in the (k,c) model of ρ are of moderate growth, by relating this model to the Zelevinsky model of ρ, and obtain as a consequence a bound for the restriction of these functions to the standard Levi subgroup associated with the composition (ck) of kc. As applications, we study convergence problems of several integrals involving (k,c) models: integrals from the generalized doubling method, and a new family of integrals which extends the Rankin--Selberg integrals for Speh representations of Lapid and Mao.

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Cite

BibTeXRIS
BibTeX
@misc{kaplan2026bounds,
  title = {{Bounds for (k,c) model functions over p-adic fields}},
  author = {Eyal Kaplan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14744},
  eprint = {2610.14744},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14744},
}
RIS
TY  - UNPB
TI  - Bounds for (k,c) model functions over p-adic fields
AU  - Eyal Kaplan
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14744
UR  - https://arxiv.org/abs/2610.14744
AB  - Let F be a p-adic field, let k,c≥1, and let ρ be a (k,c) representation of GL_kc(F): a complex representation of finite length whose wave front set has (k^c) as its unique maximal orbit, and which admits a (k,c) functional that is unique up to scaling. We prove that the functions in the (k,c) model of ρ are of moderate growth, by relating this model to the Zelevinsky model of ρ, and obtain as a consequence a bound for the restriction of these functions to the standard Levi subgroup associated with the composition (c^k) of kc. As applications, we study convergence problems of several integrals involving (k,c) models: integrals from the generalized doubling method, and a new family of integrals which extends the Rankin--Selberg integrals for Speh representations of Lapid and Mao.
ER  -