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.
Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$
On the Unicity and the Ambiguity of Lusztig Parametrizations for Finite Classical Groups
Broue's Abelian Defect Group Conjecture for the Tits Group
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