Representations of finite special linear groups in non-defining characteristic

Abstract

We classify irreducible modules over the finite special linear group SL n ( q ) in the non-defining characteristic ℓ, describe restrictions of irreducible modules from GL n ( q ) to SL n ( q ) , classify complex irreducible characters of SL n ( q ) irreducible modulo l, and discuss unitriangularity of the l-decomposition matrix for SL n ( q ) .