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Single conjugacy classes of isometries in orthogonal groups over local fields

Number Theory 2026-02-25 v1

Abstract

All isometries σ\sigma in a quadratic space over a non-archimedean local field of characteristic not 2 satisfying that any isometry τ\tau which is conjugate to σ\sigma in the general linear group is conjugate to σ\sigma in the orthogonal group are determined. This extends \cite[Theorem 2.1]{Mil} to arbitary cases.

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Cite

@article{arxiv.2602.20481,
  title  = {Single conjugacy classes of isometries in orthogonal groups over local fields},
  author = {Fei Xu and Bo Zhang},
  journal= {arXiv preprint arXiv:2602.20481},
  year   = {2026}
}