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 $R_{{\mathfrak{I}}_2(n)}^{(2,0)}$. 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 $R_{{\mathfrak{I}}_2(n)}^{(k,j)}$.

arXiv comment15 pages, 2 figures, comments are welcome