Speaker: Martin Wagner (Kaiserslautern)
Title: Generic Character Tables for Julia
Abstract:
For certain families of finite groups like \(\text{GL}_2(\mathbb{F}_q)\) it is possible to determine a so called generic character table which somehow contains the ordinary character table for every group in the family. The entries of generic character tables are sums of so called generic roots of unity which we will also call generic cyclotomic numbers or simply generic cyclotomics. With the computer algebra project CHEVIE it is possible to work with these generic character tables. Unfortunately CHEVIE relies on the proprietary computer algebra system Maple which isn't very accessible. So the part of CHEVIE depending on Maple has been ported to Julia, a modern open source programming language. In this talk we will take a closer look at this new implementation called GenericCharacterTables.jl, compare it to CHEVIE and briefly discuss some general problems with the arithmetic of generic cyclotomics.