Representations of finite special linear groups in non-defining characteristic

Details Representations of finite special linear groups in non-defining characteristic Representations of finite special linear groups in non-defining characteristic

2008-10-05

arxiv.org/abs/0810.0849v1

Mathematics

Representation Theory

24 pages. Advances in Mathematics, to appear

Scientific paper

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

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