Brauer's Height Zero Conjecture for Central Quotients of Special Linear and Special Unitary Groups

Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8

“…By results of Blau and Ellers in [6], Brauer's height zero conjecture holds for all blocks in non-defining characteristic of quasi-simple groups of type A and 2 A, and hence so does Alperin's weight conjecture for all blocks of these groups in odd characteristic with an elementary abelian defect group of order 8, by Landrock's results quoted in Proposition 3.2. This proves in particular Theorem 1.1 for these groups.…”

“…This proves in particular Theorem 1.1 for these groups. For future reference, and using methods similar to those in [6], we prove in this and the following section that elementary abelian 2-defect groups of odd rank at least three do not occur in type A and type 2 A, and that blocks with an elementary abelian 2-defect group of even rank at least four of these groups satisfy Alperin's weight conjecture. For the remainder of the paper, we assume p = 2.…”

Brauer's height zero conjecture for quasi-simple groups

“…We may hence suppose that is a non-defining prime. There, Brauer's height zero conjecture for groups of type A n has been shown by Blau and Ellers [1]. For all the other types, the claim is shown in Theorem 2.20.…”

Local-global conjectures in the representation theory of finite groups

“…The case of groups of Lie type in their defining characteristic is easy for this questions, as defect groups are either Sylow p-subgroups or trivial, and Sylow p-subgroups are non-abelian unless we are in the case of PSL 2 (q). For non-defining characteristic, Blau and Ellers [9] obtained the following important result:…”