Symmetric powers of representations of finite groups
The main result is that if \(V\) is a finite dimensional faithful module for a finite group \(G\) over a field \(K\) and \(c\) is the number of elements of \(G\) which have scalar action on \(V\) then, for large values of \(n\), the sum of \(c\) consecutive symmetric powers \(S_n(V) \oplus S_{n + 1} (V) \oplus \cdots \oplus S_{n + c - 1} (V)\) is close to being a free \(KG\)- module. A similar result holds for metabelian Lie powers.
scientific article; zbMATH DE number 168591