The homology of certain subgroups of the symmetric group with coefficients in \(\text{Lie}(n)\)
Based on earlier work of the first author with \textit{M. Mahowald} [Invent. Math. 135, No. 3, 743--788 (1999; Zbl 0997.55016)] calculating the homology \(H_*(\Sigma_n,{\mathcal L}ie(n))\) of the symmetric group with coefficients in a certain Lie algebra over \({\mathbb Z}/p\), the authors calculate the homology of subgroups of the form \(\Sigma_{n_1} \times \cdots \times \Sigma_{n_k}\) with \(n_1+ \cdots+ n_k=n\), with the same coefficients. The approach is via homotopy theory and relies on Goodwillie's calculus of functors.
scientific article; zbMATH DE number 1308150