Weyl modules for the Schur algebra of the alternating group

Let F be the field of complex numbers and V=V0 V1 a vector space over F with dimV0=dimV1. The symmetric group acts on V n by the sign-permutation action [Berele, Regev, Adv. in Math. 46 (2) (1987)]. Let S*(V,n) SA*(V,n) be the corresponding Schur algebras of Sn and of An Sn, respectively, where An is the alternating group [Regev, J. Algebra, in print]. Following the fundamental work of H. Weyl, the explicit decomposition of V n as an S*(V,n)-module was given in [Berele, Regev, Adv. in Math. 46 (2) (1987)]. By applying the character theory and the representation theory of An we give here the explicit decomposition of V n as an SA*(V,n)-module.