A 2-basic set of the alternating group

摘要

In this note, we construct a 2-basic set of the alternating group U_n. To do this, we construct a 2-basic set of the symmetric group G _{with an additional property, such that its restriction to U_n is a 2-basic set. We adapt here a method developed by Brunat and Gramain (J. Reine Angew. Math., to appear) for the case when the characteristic is odd. One of the main tools is the generalized perfect isometries defined by Külshammer et al. (Invent. Math. 151, 513-552, (2003)).}