2-Dimensional vector invariants of parabolic subgroups of Gl2(Fp) over the field Fp Original Research Article

Given a group G acting on a finite dimensional vector space V over any field k, we ask for the structure of the ring of invariants of the diagonal action of the group on the symmetric algebra of m copies of V, the so-called m-dimensional vector invariants of G. In this paper we use elementary techniques to determine the structure of the 2-dimensional vector invariants of Gl2(FP), Sl2(FP), U2(FP) acting as usual on a vector space of dimension 2 over FP. We know that these rings of invariants are Cohen-Macaulay and we compute for each a free module basis over a suitably chosen homogeneous system of parameters.