On the character of certain modular irreducible representations

TL;DR

This paper revisits a longstanding conjecture about the characters of irreducible modular representations of algebraic groups over fields of positive characteristic, aiming to make it more broadly applicable.

Contribution

It reformulates a 1979 conjecture on the characters of irreducible modular representations to apply directly to any dominant highest weight.

Findings

Restates and clarifies the conjecture for broader applicability

Provides a new formulation relevant to all dominant highest weights

Lays groundwork for future verification or proof

Abstract

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it is now directly applicable to any dominant highest weight.