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|Title:||On functorial decompositions of self-smash products|
|Citation:||Selick, P., Wu, J. (2003-08). On functorial decompositions of self-smash products. Manuscripta Mathematica 111 (4) : 435-457. ScholarBank@NUS Repository. https://doi.org/10.1007/s00229-002-0353-1|
|Abstract:||We give a decomposition formula for n -fold self smash of a two-cell suspension X localized at 2. The mod 2 homology of each factor in the decomposition is explicitly given as a module over the Steenrod algebra and in the case where X is formed by suspending one of ℝP2, ℂP2, ℍP2 or double-struck K sign P2, this is a complete decomposition into indecomposable pieces. The method has consequences in the modular representation theory of the symmetric group where it leads to a computation of the submatrix for the decomposition matrix of the group algebra ℤ/2[Sn] which correspond to partitions of length 2. In particular this yields a derivation of the explicit formula due to Erdmann which gives the multiplicities in the decomposition of ℤ/2[S n] of the indecomposable projective modules which correspond to those partitions.|
|Source Title:||Manuscripta Mathematica|
|Appears in Collections:||Staff Publications|
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