Representations of finite special linear groups in non-defining characteristic

Alexander S. Kleshchev; Pham Huu Tiep

paper

Representations of finite special linear groups in non-defining characteristic

arXiv:0810.0849

Abstract

We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $G L_{n} (q)$ on restriction to $S L_{n} (q)$ . Combined with a recent result of C. Bonnafe, this yields a canonical labeling for irreducible $ℓ$ -modular representations of $S L_{n} (q)$ , where $(ℓ, q) = 1$ . As an application, we classify for the first time complex representations of $S L_{n} (q)$ whose reductions modulo $ℓ$ are irreducible.

24 pages. Advances in Mathematics, to appear