Irreducible Characters for Algebraic Groups in Characteristic Three

TL;DR

This paper computes the irreducible characters of simple algebraic groups of type A_5 over fields of characteristic 3, using a modified algorithm and computational tools to improve efficiency.

Contribution

It introduces a new, faster algorithm for computing irreducible characters of algebraic groups in characteristic 3, building on Xi Nanhua's theorem and MATLAB.

Findings

Successfully determined irreducible characters for type A_5 in characteristic 3

Enhanced computational efficiency over previous methods

Validated results with theoretical and software tools

Abstract

In this note, we determine the irreducible characters for the simple algebraic groups of type $A_5$ over an algebraically closed field $K$ of characteristic 3, by using a theorem of Xi Nanhua and the Matlab software. In order to obtain higher speed than in Jiachen et al we modify the algorithm to compute the irreducible characters.