Mathematics – Representation Theory
Scientific paper
2008-10-10
Journal f\"ur die reine und angewandte Mathematik 641 (2010), 177-202
Mathematics
Representation Theory
Scientific paper
This article concerns the $p$-basic set existence problem in the representation theory of finite groups. We show that, for any odd prime $p$, the alternating group $\A_n$ has a $p$-basic set. More precisely, we prove that the symmetric group $\sym_n$ has a $p$-basic set with some additional properties, allowing us to deduce a $p$-basic set for $\A_n$. Our main tool is the generalized perfect isometries introduced by K\"ulshammer, Olsson and Robinson. As a consequence we obtain some results on the decomposition number of $\A_n$.
Brunat Olivier
Gramain Jean-Baptiste
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