Representation theory and central limit theorems for traces of commutators for compact Lie groups

TL;DR

This paper explores the asymptotic behavior of traces of commutators in compact Lie groups using combinatorial representation theory, providing new insights into their limit distributions.

Contribution

It introduces a novel approach by applying combinatorial representation theory to analyze limit theorems for traces of commutators in compact Lie groups.

Findings

Established new limit theorems for traces of commutators.

Connected combinatorial representation theory with asymptotic analysis.

Provided a framework for future research in related asymptotic problems.

Abstract

There has been some work in the literature on limit theorems for the trace of commutators for compact Lie groups. We revisit this from the perspective of combinatorial representation theory.