Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic

Shintani descent and perfect isometries for blocks of finite general linear groups

“…Also, in several special cases, it has been proved that the blocks b and c are in fact Morita equivalent (see, for instance, [9,12]); the fact that there is a sign preserving isometry between them is an immediate consequence.…”

Filtrations in Rouquier Blocks of Symmetric Groups and Schur Algebras

“…An analogue of the Morita equivalence of B w and A(w) for finite general linear groups has been proved independently by Turner [25] and by Miyachi [22]. Hida and Miyachi [8] have then used this to prove analogues of Proposition 4.4, the last statement in Theorem 5.2, and the second statement of Theorem 6.2.…”

Local-global conjectures in the representation theory of finite groups

“…In their landmark paper [28] Chuang and Rouquier have given a proof of Broué's conjecture for S n and for GL n (q), building on previous results of Chuang and Kessar [27] and Turner [97] who obtained derived equivalences for a very particular class of blocks, the so-called Rouquier blocks. Dudas, Varagnolo and Vasserot [34] have constructed derived equivalences between blocks of various finite unitary groups which together with a result of Livesey [58] provides a verification of Broué's conjecture for GU n (q) for linear primes.…”