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Langlands-Shahidi gamma factors and local transfer in families

  • Johannes Girsch
  • Robert Kurinczuk
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Abstract

Let G be a quasi-split p-adic group, defined over a non-archimedean local field of residue cardinality q, and R be a ℤ[√q−1,μ4p∞]-algebra. We generalize the constructions of Shahidi local coefficients and Langlands-Shahidi gamma factors to the setting of co-Whittaker R-representations. For classical p-adic groups, we prove there is a unique integral morphism of endomorphism rings of Gelfand--Graev representations, interpolating the (standard) local generic transfer to a general linear group. This yields a local transfer morphism in families, which allows us to deduce properties of the local ℓ-adic generic transfer and congruences modulo primes ℓ≠ p.

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Cite

BibTeXRIS
BibTeX
@misc{girsch2026langlandsshahidi,
  title = {{Langlands-Shahidi gamma factors and local transfer in families}},
  author = {Johannes Girsch and Robert Kurinczuk},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31615},
  eprint = {2610.31615},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31615},
}
RIS
TY  - UNPB
TI  - Langlands-Shahidi gamma factors and local transfer in families
AU  - Johannes Girsch
AU  - Robert Kurinczuk
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31615
UR  - https://arxiv.org/abs/2610.31615
AB  - Let G be a quasi-split p-adic group, defined over a non-archimedean local field of residue cardinality q, and R be a ℤ[√q^−1,μ_4p^∞]-algebra. We generalize the constructions of Shahidi local coefficients and Langlands-Shahidi gamma factors to the setting of co-Whittaker R-representations. For classical p-adic groups, we prove there is a unique integral morphism of endomorphism rings of Gelfand--Graev representations, interpolating the (standard) local generic transfer to a general linear group. This yields a local transfer morphism in families, which allows us to deduce properties of the local ℓ-adic generic transfer and congruences modulo primes ℓ≠ p.
ER  -