A ug 2 00 4 Modular Lie Powers and the Solomon descent algebra

@inproceedings{Erdmann2008AU2,
  title={A ug 2 00 4 Modular Lie Powers and the Solomon descent algebra},
  author={Karin Erdmann},
  year={2008}
}
Let V be an r-dimensional vector space over an infinite field F of prime characteristic p, and let Ln(V ) denote the n-th homogeneous component of the free Lie algebra on V . We study the structure of Ln(V ) as a module for the general linear group GLr(F ) when n = pk and k is not divisible by p and where n ≥ r. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of Lk(V ) and the indecomposable direct summands of Ln(V ) which… CONTINUE READING