Basic sets for unipotent blocks of finite reductive groups in bad characteristic

TL;DR

This paper establishes the existence of a unitriangular basic set for unipotent blocks in certain finite reductive groups in bad characteristic, introduces an algorithm for counting unipotent Brauer characters, and verifies its effectiveness.

Contribution

It proves the existence of a basic set in specific cases and develops an effective algorithm for counting unipotent Brauer characters in exceptional groups.

Findings

Existence of a unitriangular basic set for unipotent blocks in classical types

An algorithm for counting irreducible unipotent Brauer characters

Verification of the algorithm's effectiveness in exceptional groups

Abstract

We show the existence of a unitriangular basic set for unipotent blocks simple reductive groups of classical type in bad characteristic with some exceptions. Then,we introduce an algorithm to count irreducible unipotent Brauer characters and we verify that this algorithm is effective for exceptional adjoint groups.