Adjoint and coadjoint orbits of the Poincar\'e group
Representation Theory
2024-10-08 v5
Abstract
In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we classify the adjoint and coadjoint orbits of the Poincar\'{e} group.
Keywords
Cite
@article{arxiv.math/0305442,
title = {Adjoint and coadjoint orbits of the Poincar\'e group},
author = {Richard Cushman and Wilberd van der Kallen},
journal= {arXiv preprint arXiv:math/0305442},
year = {2024}
}
Comments
Revised arguments in section 6, results unchanged. Corrected typos