GenericCharacterTables.jl

About

GenericCharacterTables is a library for working with generic character tables. It is based on CHEVIE and aims to provide all its features originally implemented in Maple. It is written in Julia and depends on Nemo and therefore on AbstractAlgebra.

For the mathematical background, consider that there are many interesting families of finite groups. For example, the matrix groups $\mathrm{GL}_n(\mathbb{F}_q)$ or $\mathrm{SL}_n(\mathbb{F}_q)$, for $n>1$ and $q$ a prime power. These groups have many properties in common. It turns out that for a fixed rank (say $n=2$) it is possible to parametrize the conjugacy classes and irreducible characters of these group in terms of $q$, and to write this down into a so-called generic character table. This was first done by Schur for $\mathrm{SL}_2(\mathbb{F}_q)$.

This package provides code to interact with such generic character tables, and also includes many such tables. The code in this package is based on Maple code included in the CHEVIE project.

For more details about the mathematical background, see [GHLMP96].