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PreprintarXiv licencearXiv

Base change and the Mackey formula in Deligne--Lusztig theory

  • Sean Cotner
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Abstract

Using ideas of Digne and recent work of Gaitsgory--Rozenblyum--Varshavsky, we show that Lusztig induction commutes with (a minor variant of) the Glauberman correspondence for large prime degree field extensions. This allows one to reduce the Mackey formula in Deligne--Lusztig theory to the case of ``large'' base fields, in which case the result is due to Bonnafé.

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Cite

BibTeXRIS
BibTeX
@misc{cotner2026base,
  title = {{Base change and the Mackey formula in Deligne--Lusztig theory}},
  author = {Sean Cotner},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22331},
  eprint = {2609.22331},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22331},
}
RIS
TY  - UNPB
TI  - Base change and the Mackey formula in Deligne--Lusztig theory
AU  - Sean Cotner
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.22331
UR  - https://arxiv.org/abs/2609.22331
AB  - Using ideas of Digne and recent work of Gaitsgory--Rozenblyum--Varshavsky, we show that Lusztig induction commutes with (a minor variant of) the Glauberman correspondence for large prime degree field extensions. This allows one to reduce the Mackey formula in Deligne--Lusztig theory to the case of ``large'' base fields, in which case the result is due to Bonnafé.
ER  -