On commutator fibers over regular semisimple and central elements of $SL_n$

TL;DR

This paper calculates irreducible character values of $G_n$ to estimate the size of fibers of the commutator map over regular semisimple and central elements of $ ext{SL}_n$, providing detailed algebraic insights.

Contribution

It provides detailed calculations of irreducible character values to estimate fiber sizes of the commutator map in $ ext{SL}_n$, advancing understanding of algebraic structures.

Findings

Estimated fiber sizes over regular semisimple elements

Estimated fiber sizes over central elements

Detailed character value calculations

Abstract

We account some detailed calculation of irreducible character values of $G_n$ with application to estimate fiber size of the commutator map over regular semisimple and central elements of $\SL_n$.