On the averages of characteristic polynomials from classical groups

TL;DR

This paper derives formulas for products and ratios of characteristic polynomials from classical groups using classical mathematical results, providing an elementary and self-contained approach.

Contribution

It offers a new, simplified derivation of characteristic polynomial averages for classical groups, enhancing understanding and accessibility.

Findings

Derived explicit formulas for characteristic polynomial products and ratios

Utilized classical results from Weyl and Littlewood in derivations

Presented an elementary, self-contained proof approach

Abstract

We provide an elementary and self-contained derivation of formulae for products and ratios of characteristic polynomials from classical groups using classical results due to Weyl and Littlewood.