Single conjugacy classes of isometries in orthogonal groups over local fields
Number Theory
2026-02-25 v1
Abstract
All isometries in a quadratic space over a non-archimedean local field of characteristic not 2 satisfying that any isometry which is conjugate to in the general linear group is conjugate to in the orthogonal group are determined. This extends \cite[Theorem 2.1]{Mil} to arbitary cases.
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}
}