Characteristic Polynomials and Fixed Spaces of Semisimple Elements

TL;DR

This paper extends previous results on the fixed point spaces of elements in irreducible linear groups by analyzing characteristic polynomials, providing new insights into the structure of semisimple elements.

Contribution

It introduces an approach focusing on characteristic polynomials to study fixed spaces, advancing understanding beyond prior fixed space dimension results.

Findings

Extended results on fixed point spaces using characteristic polynomials

Provided new bounds or descriptions for semisimple elements

Answered a specific question posed by Frank Calegari

Abstract

Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.