On sums of admissible coadjoint orbits

TL;DR

This paper characterizes the possible spectra resulting from summing two admissible elements in the dual space of a quasi-Hermitian semisimple Lie algebra, extending understanding of their spectral properties.

Contribution

It provides a description of the spectra of sums of admissible elements in the dual space of quasi-Hermitian semisimple Lie algebras, a novel spectral analysis.

Findings

Characterization of spectra of sums of admissible elements

Extension of spectral theory in quasi-Hermitian semisimple Lie algebras

New criteria for admissibility and spectral sums

Abstract

Given a quasi-Hermitian semisimple Lie algebra, we describe possible spectra of the sum of two admissible elements from its dual vector space.