On Rouquier Blocks for Finite Classical Groups at Linear Primes

TL;DR

This paper extends the understanding of Rouquier blocks by demonstrating their existence in finite classical groups at linear primes, building on prior results for general linear groups.

Contribution

It proves that finite classical groups also have unipotent Rouquier blocks at linear primes, expanding the scope of Broue's Abelian Defect Group Conjecture.

Findings

Finite classical groups possess unipotent Rouquier blocks at linear primes.

The results generalize previous findings from general linear groups.

Supports Broue's Abelian Defect Group Conjecture for broader classes of groups.

Abstract

H. Miyachi and W. Turner have independently proved that Broue's Abelian Defect Group Conjecture holds for certain unipotent blocks of the finite general linear group, the so-called Rouquier blocks. This together with A. Marcus and J. Chuang and R. Rouquier proves that the conjecture holds for all blocks of such groups. We prove that other finite classical groups also possess unipotent Rouquier blocks at linear primes.