Gröbner bases for the Hilbert ideal and coinvariants of the dihedral group D2p

Abstract

We consider a finite dimensional representation of the dihedral group D2p over a field of characteristic two where p is an odd integer and study the corresponding Hilbert ideal IH . We show that IH has a universal Grobner basis consisting of invariants and monomials only. We provide sharp bounds for the degree of an ¨ element in this basis and in a minimal generating set for IH . We also compute the top degree of coinvariants when p is prime.