Specht ideals are symmetric ideals in the polynomial ring generated by Specht polynomials associated with group representations. These ideals were previously studied for reflection groups of types A and B, where their inclusion relations and their varieties reflect rich combinatorial structures. In this paper, we extend this theory to type D and the dihedral groups. Our results complete the combinatorial study of Specht ideals across all infinite families of essential real reflection groups.
Debus et al. (Wed,) studied this question.