The unbroken spectra of Frobenius seaweeds

TL;DR

This paper demonstrates that Frobenius seaweed Lie algebras have spectra of principal elements that form continuous integer sets with symmetric multiplicities, using combinatorial methods.

Contribution

It introduces a combinatorial approach to analyze the spectra of principal elements in Frobenius seaweed Lie algebras, revealing their unbroken integer spectra and symmetry.

Findings

Spectra are unbroken sets of integers.

Spectra multiplicities are symmetrically distributed.

Methods are combinatorial.

Abstract

We show that if $\mathfrak{g}$ is a Frobenius seaweed, then the spectrum of the adjoint of a principal element consists of an unbroken set of integers whose multiplicities have a symmetric distribution. Our methods are combinatorial.