Turning Weight Multiplicities into Brauer Characters

TL;DR

This paper introduces two methods to compute $p$-modular Brauer character tables for groups of Lie type, leveraging known ordinary character tables and weight multiplicities, enhancing computational tools in representation theory.

Contribution

It presents novel algorithms that utilize weight multiplicities and ordinary character data to efficiently determine Brauer character tables for groups of Lie type.

Findings

Methods successfully compute Brauer tables in tested cases.

Algorithms improve computational efficiency over previous approaches.

Provides a framework for future calculations in modular representation theory.

Abstract

We describe two methods for computing $p$-modular Brauer character tables for groups of Lie type $G(p^f)$ in defining characteristic $p$, assuming that the ordinary character table of $G(p^f)$ is known, and the weight multiplicities of the corresponding algebraic group $G$ are known for $p$-restricted highest weights.