English

Real adjoint orbits of special linear groups

Group Theory 2024-04-25 v3

Abstract

Let G G be a Lie group with Lie algebra g \mathfrak{g} . An element Xg X \in \mathfrak{g} is called AdG\mathrm{Ad}_G-real if X=gXg1 -X=gXg^{-1} for some gG g \in G . Moreover, if X=gXg1 -X=gXg^{-1} holds for some involution gG g\in G , then X X is called strongly AdG\mathrm{Ad}_G-real. We have classified the AdG\mathrm{Ad}_G-real and the strongly AdG\mathrm{Ad}_G-real orbits in the special linear Lie algebra sl(n,F)\mathfrak{sl}(n,\mathbb{F}) for F=C \mathbb{F}=\mathbb{C} or H\mathbb{H} .

Keywords

Cite

@article{arxiv.2204.03624,
  title  = {Real adjoint orbits of special linear groups},
  author = {Krishnendu Gongopadhyay and Tejbir Lohan and Chandan Maity},
  journal= {arXiv preprint arXiv:2204.03624},
  year   = {2024}
}

Comments

Final version, 17 pages, To appear in Illinois Journal of Mathematics

R2 v1 2026-06-24T10:41:33.466Z