A Conjectural Algorithm for Simple Characters of Algebraic Groups

TL;DR

This paper presents an algorithm that computes simple module characters for algebraic groups based on tilting module characters, assuming Donkin's conjecture holds, applicable across all characteristics.

Contribution

It introduces a conjectural algorithm that leverages tilting module characters to determine simple module characters, contingent on Donkin's tilting conjecture.

Findings

Algorithm computes simple characters assuming Donkin's conjecture

Works for algebraic groups in any characteristic

Provides a practical method under conjectural assumptions

Abstract

We describe an algorithm, which - given the characters of tilting modules and assuming that Donkin's tilting conjecture is true - computes the characters of simple modules for an algebraic group in any characteristic.