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A note on rational wavefront sets for finite special orthogonal groups

  • Pengcheng Li
  • Zhicheng Wang
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Abstract

We study rational wavefront sets of irreducible representations of finite special orthogonal groups over 𝔽q. We assume that q is odd and that both q and its characteristic are sufficiently large. Using {the second author's} results for full orthogonal groups, we determine the maximal rational wavefront sets and the dimensions of the corresponding generalized Whittaker models. We show that each rational wavefront set is the rational closure of its maximal elements. For unipotent representations, we describe the maximal rational wavefront sets in terms of Lusztig's canonical quotient and their behavior under Alvis--Curtis duality.

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Cite

BibTeXRIS
BibTeX
@misc{li2026note,
  title = {{A note on rational wavefront sets for finite special orthogonal groups}},
  author = {Pengcheng Li and Zhicheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41741},
  eprint = {2610.41741},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41741},
}
RIS
TY  - UNPB
TI  - A note on rational wavefront sets for finite special orthogonal groups
AU  - Pengcheng Li
AU  - Zhicheng Wang
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41741
UR  - https://arxiv.org/abs/2610.41741
AB  - We study rational wavefront sets of irreducible representations of finite special orthogonal groups over 𝔽_q. We assume that q is odd and that both q and its characteristic are sufficiently large. Using {the second author's} results for full orthogonal groups, we determine the maximal rational wavefront sets and the dimensions of the corresponding generalized Whittaker models. We show that each rational wavefront set is the rational closure of its maximal elements. For unipotent representations, we describe the maximal rational wavefront sets in terms of Lusztig's canonical quotient and their behavior under Alvis--Curtis duality.
ER  -