Universal series for dihedral group coinvariant rings

Abstract

In 1994, Alfano determined a monomial basis, bigraded Hilbert series, and bigraded Frobenius series for the ring of diagonal dihedral group coinvariants $R^{(2,0)}_{\mathfrak{I}_{2}(n)}$. Using diagonal supersymmetry, we determine a universal multigraded character series, universal multigraded Hilbert series, and monomial basis for the generalization to any $k$ sets of bosonic variables and $j$ sets of fermionic variables $R^{(k,j)}_{\mathfrak{I}_{2}(n)}$.