On the generalized Burnside ring with respect to the Young subgroups of the symmetric group (Q5929453)

The authors show that the number of blocks of the generalized Burnside algebra in finite characteristic \(p\) of the symmetric group \(S_n\) with respect to the Young subgroups is equal to the number of simple \(kS_n\)-modules, where \(k\) is a field of characteristic \(p\). As a corollary, one gets a new proof that for any field \(F\) of characteristic \(p\), the representation algebra of \(kS_n\) with coefficients in \(F\) is semisimple.