On the decomposition map for symmetric groups.
Let \(R^d\) be the \(\mathbb{Z}\)-module generated by the irreducible characters of the symmetric group \(\mathcal S_d\). In this interesting paper, the author gives a basis for the kernel of the decomposition map in terms of certain symmetric functions. She also proves that when \(F\) has prime characteristic and \(I_{br}^d\) is the kernel of the decomposition map for prime \(p\) then \(R^d/I_{br}^d\otimes_\mathbb{Z} F\) is isomorphic to the radical quotient of the \(p\)-modular Solomon descent algebra.
scientific article; zbMATH DE number 5566030