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PreprintarXiv licencearXiv

Effective results in representation theory of reductive groups over local fields

  • Avraham Aizenbud
  • Dmitry Gourevitch
  • David Kazhdan
  • Eitan Sayag
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Abstract

We prove effective versions of several classical results in representation theory of reductive groups over non-Archimedean local fields of arbitrary characteristic. More specifically, we deal with the support of matrix coefficients of cuspidal representations and the recursions satisfied by matrix coefficients of representations of finite length. We provide effective generation results for irreducible representations. Finally, we study the effective smoothness of characters on the set of regular semi-simple elements.

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Cite

BibTeXRIS
BibTeX
@misc{aizenbud2026effective,
  title = {{Effective results in representation theory of reductive groups over local fields}},
  author = {Avraham Aizenbud and Dmitry Gourevitch and David Kazhdan and Eitan Sayag},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04659},
  eprint = {2611.04659},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04659},
}
RIS
TY  - UNPB
TI  - Effective results in representation theory of reductive groups over local fields
AU  - Avraham Aizenbud
AU  - Dmitry Gourevitch
AU  - David Kazhdan
AU  - Eitan Sayag
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04659
UR  - https://arxiv.org/abs/2611.04659
AB  - We prove effective versions of several classical results in representation theory of reductive groups over non-Archimedean local fields of arbitrary characteristic. More specifically, we deal with the support of matrix coefficients of cuspidal representations and the recursions satisfied by matrix coefficients of representations of finite length. We provide effective generation results for irreducible representations. Finally, we study the effective smoothness of characters on the set of regular semi-simple elements.
ER  -