Quasi-invariant and super-covariant polynomials for the generalized symmetric group.

    Jean-Christophe Aval, LaBRI, Bordeaux

The generalized symmetric group G(n,m) may be viewed
as the group of square matrices of size n having one
non-zero entry in each row and column, this entry being
a m-th root of unity. We will talk about two action
of the (generalized) symmetric group on polynomials
(symmetrizing and quasi-symmetrizing action) and
will study their invariants and covariants (quotient
by invariants). We will make and important use of
Grobner bases.