Mara Neusel

Abstract:   Let ρ: G → GL(n, F) be a permutation representation of a finite group G. We study the number of orbits of special monomials of G acting on the polynomials in n variables via ρ. We will present formulae for several crucial families of groups, for direct sums of representations, as well as for vector invariants. In addition we will see two algorithms for arbitrary permutation groups, one relying on the geometry of G acting on V = Fⁿ, the other relying on the representation theory of the symmetric groups.
        This is joint work with Chris Monico.

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