An upper bound on the exceptional characteristics for Lusztig's character formula

TL;DR

This paper establishes an explicit upper bound on the exceptional characteristics relevant to Lusztig's character formula for reductive algebraic groups, using a combinatorial Lefschetz theory.

Contribution

It introduces a combinatorial Lefschetz theory to derive an explicit, large upper bound on exceptional characteristics for Lusztig's formula.

Findings

Derived an explicit upper bound on exceptional characteristics

Bound is significantly larger than the Coxeter number

Provided a combinatorial framework for the analysis

Abstract

We develop and study a Lefschetz theory in a combinatorial category associated to a root system and derive an upper bound on the exceptional characteristics for Lusztig's formula for the simple rational characters of a reductive algebraic group. Our bound is huge compared to the Coxeter number. It is, however, given by an explicit formula.