On functorial decompositions of self-smash products

P. Selick and J. Wu

Abstract. We give a decomposition formula for n-fold self smash of a 
two-cell suspension X localized at 2, in which the mod 2 homology of 
each factor in the decomposition is explicitly given and is indecomposable
over the Steenrod algebra if X is a suspension of RP^2, CP^2, HP^2 or KP^2.
Furthermore, we give an explicit formula for the multiplicity of 
indecomposable projective symmetric group modules over Z/2 which correspond
to two-row Young diagrams. Moreover we give an explicit formula to compute
the submatrix of the decomposition matrix of symmetric group algebra over
Z/2 corresponding to two-row Young diagrams.