On the character of certain tilting modules

TL;DR

This paper proposes a simple, partly conjectural formula for the characters of many indecomposable tilting modules of a semisimple algebraic group over a field of positive characteristic, assuming the characteristic is large.

Contribution

It introduces a new, simplified formula for tilting module characters in the context of algebraic groups over fields of large characteristic.

Findings

Proposes a conjectural formula for tilting module characters

Applicable to many indecomposable tilting modules

Assumes large characteristic p

Abstract

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.