Weingarten calculus for matrix ensembles associated with compact symmetric spaces

TL;DR

This paper introduces a method using Weingarten calculus to compute polynomial integrals over compact symmetric spaces, expressing results as sums over symmetric groups, advancing the mathematical tools for such integrals.

Contribution

It develops a novel approach for calculating integrals on symmetric spaces using Weingarten calculus, linking group theory with integral computation.

Findings

Provides explicit formulas for integrals on symmetric spaces

Expresses integrals as sums over symmetric groups

Enhances computational techniques for symmetric space analysis

Abstract

A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.