Macdonald formula, Ricci Curvature, and Concentration Locus for classical compact Lie groups

TL;DR

This paper explores the use of Macdonald's formula and Ricci curvature to analyze concentration loci in classical compact Lie groups, providing insights into measure concentration phenomena in these mathematical structures.

Contribution

It introduces a novel approach combining Macdonald's formula and Ricci curvature to study measure concentration in classical compact Lie groups.

Findings

Identification of concentration loci in classical compact Lie groups

Application of Ricci curvature to measure concentration analysis

New insights into geometric measure concentration phenomena

Abstract

For Classical compact Lie groups, we use Macdonald's formula \cite{Ma} and Ricci curvature for analyzing a "concentration locus", which is a tool to detect where a sequence of metric, Borel measurable spaces concentrates its measure.