On decomposition numbers and Alvis-Curtis duality

Details On decomposition numbers and Alvis-Curtis duality On decomposition numbers and Alvis-Curtis duality

2007-09-20

arxiv.org/abs/0709.3223v2

Mathematics

Representation Theory

to appear in Math. Proc. Cam. Philos. Soc

Scientific paper

We show that for general linear groups ${\rm GL}_n(q)$ as well as for
$q$-Schur algebras the knowledge of the modular Alvis-Curtis duality over
fields of characteristic $\ell$, $\ell \nmid q$, is equivalent to the knowledge
of the decomposition numbers.

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