The Irreducible Brauer Characters of the Finite Special Linear Groups in Non-describing Characteristics

Generalized q-Schur algebras and modular representation theory of finite groups with split (BN)-pairs

“…We get a complete description of the module structure of the so called Steinberg lattice, that is the unique quotient lattice of the Gelfand-Graev lattice affording the Steinberg character. In case of general linear groups, the corresponding quotient of the Gelfand-Graev lattice affording other irrducible characters (even for those characters not lying in ℓ-regular Lusztig series) are described in [26]. There, also for the special linear groups corresponding results have been obtained.…”

“…As a standard example for this to happen we can consider the finite special linear groups. These groups were treated in [26]. There it was shown how one can describe the decomposition matrix of a set of irreducible characters whose reduction modulo ℓ generate the group of generalized Brauer characters in terms of decomposition matrices of q-Schur algebras defined over extended Weyl groups of type A.…”

Representations of finite special linear groups in non-defining characteristic

“…This question is important for Aschbacher-Scott program [1,23] on classifying maximal subgroups in finite classical groups and has been our original motivation, see [21]. Although representations of SL n (q) in non-defining characteristic were studied in [15] using a different approach, it is not clear how to use [15] to describe irreducible restrictions from GL n (q) to SL n (q).…”