Adjoint orbits of real affine Lie algebras

TL;DR

This paper classifies the adjoint orbits of real affine classical Lie algebras by introducing a new invariant called a modulus, which extends beyond traditional eigenvalue-based invariants.

Contribution

It provides a complete classification of adjoint orbits for real affine classical Lie algebras using a novel modulus parameter, surpassing classical Jordan invariants.

Findings

Each orbit has a unique representative incorporating the modulus.

The classification extends traditional eigenvalue invariants.

New methods for orbit determination in affine Lie algebras.

Abstract

In this paper we find a representative of each orbit of the adjoint action of a real affine classical group of its Lie algebra. These orbits are not determined by the usual Jordan invariants of eigenvalues and block sizes, but require a noneigenvalue parameter called a modulus.