The Gini Index in the Representation Theory of the General Linear Group

Abstract

The Gini index is a function that attempts to measure the amount of inequality in the distribution of a finite resource throughout a population. It is commonly used in economics as a measure of inequality of income or wealth. We define a discrete Gini index on the set of integer partitions with at most n parts and show how this function emerges in the representation theory of the complex general linear group.