A basic set for the alternating group

TY - JOUR

T1 - A basic set for the alternating group

AU - Brunat, O.

AU - Gramain, Jean-Baptiste Bernard

PY - 2010/4

Y1 - 2010/4

N2 - 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 Un has a p-basic set. More precisely, we prove that the symmetric group Gn has a p-basic set with some additional properties, allowing us to deduce a p-basic set for Un. Our main tool is the concept of generalized perfect isometries introduced by Külshammer, Olsson and Robinson. As a consequence we obtain some results on the decomposition numbers of Un.

AB - 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 Un has a p-basic set. More precisely, we prove that the symmetric group Gn has a p-basic set with some additional properties, allowing us to deduce a p-basic set for Un. Our main tool is the concept of generalized perfect isometries introduced by Külshammer, Olsson and Robinson. As a consequence we obtain some results on the decomposition numbers of Un.

M3 - Journal article

SN - 0075-4102

VL - 641

SP - 177

EP - 202

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

ER -