The sparsity of character tables of high rank groups of Lie type

TL;DR

This paper investigates the behavior of character tables of high rank finite simple groups of Lie type, showing that as the rank increases, the proportion of non-zero entries diminishes to zero.

Contribution

It provides an asymptotic analysis of the sparsity of character tables for high rank groups of Lie type, revealing a new property of their structure.

Findings

Fraction of non-zero entries tends to zero as rank increases

Character tables become increasingly sparse in high rank limit

Highlights a fundamental structural property of Lie type groups

Abstract

In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.