Minimal Polynomials in Spin Representations of Symmetric and Alternating Groups

TL;DR

This paper calculates the minimal polynomials of elements in the double cover of symmetric and alternating groups within all irreducible spin representations, providing detailed algebraic insights.

Contribution

It explicitly determines the minimal polynomials for elements of the double cover in all irreducible spin representations, a novel comprehensive analysis.

Findings

Explicit minimal polynomials for all elements in spin representations

Complete classification of element behavior in double covers

Enhanced understanding of spin representation algebra

Abstract

We determine the minimal polynomial of each element of the double cover $G$ of the symmetric or alternating group in every irreducible spin representation of $G$.