A basic set for the alternating group

Original · EN

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 ₙ has a p-basic set. More precisely, we prove that the symmetric group ₙ has a p-basic set with some additional properties, allowing us to deduce a p-basic set for 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 ₙ.