A Basic Set for the Alternating Group
Olivier Brunat and Jean-Baptiste Gramain

Abstract.  This article is concerned with the p-basic set existence problem in
the representation theory of finite groups. We show that, for any odd prime p,
the alternating group An has a p-basic set.  More precisely, we prove that the
symmetric group Sn has a p-basic set with some additional properties, allowing
us to deduce a p-basic set for An. Our main tool is the concept of generalized
perfect isometries introduced  by  K\"ulshammer,  Olsson  and  Robinson.  As a
consequence we obtain some results on the decomposition numbers of An.