Gregor Kemper
Universitaet Heidelberg

"Hilbert Series and Degree Bounds in Invariant Theory",
IWR-Preprint 97-45, Heidelberg 1997

Abstract:

  The Hilbert series and degree bounds play significant roles in
  computational invariant theory. In the modular case, neither of
  these tools is available in general. In this article three results
  are obtained, which provide partial remedies for these shortcomings.
  First, it is shown that the so-called extended Hilbert series, which
  can always be calculated by a Molien type formula, yields strong
  constraints on the degrees of primary invariants. Then it is shown
  that for a trivial source module the (ordinary) Hilbert series
  coincides with that of a lift to characteristic 0 and can hence be
  calculated by Molien's formula. The last result is a generalization
  of G\"obel's degree bound to the case of monomial representations.