On the Morita Frobenius numbers of blocks of finite reductive groups

TL;DR

This paper investigates the Morita Frobenius numbers of blocks in various finite groups, establishing that most have a number of 1, with some cases reaching at most 2, thus advancing understanding in modular representation theory.

Contribution

It provides new bounds and exact values for the Morita Frobenius numbers of blocks in finite groups of Lie type and related groups, expanding the theoretical framework.

Findings

Morita Frobenius number of blocks in alternating groups is 1

Most unipotent blocks in finite groups of Lie type have Morita Frobenius number 1

Remaining cases have Morita Frobenius number at most 2

Abstract

We show that the Morita Frobenius number of the blocks of the alternating groups, the finite groups of Lie type in describing characteristic, and the Ree and Suzuki groups is 1. We also show that the Morita Frobenius number of almost all of the unipotent blocks of the finite groups of Lie type in non-defining characteristic is 1, and that in the remaining cases it is at most 2.