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arXiv · 0810.1840

A basic set for the alternating group

Olivier Brunat·Jean-Baptiste Gramain
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Abstract

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 Külshammer, Olsson and Robinson. As a consequence we obtain some results on the decomposition number of $\A_n$.

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Olivier Brunat, Jean-Baptiste Gramain. 2008-10-10. A basic set for the alternating group. https://arxiv.org/abs/0810.1840

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