Signature Pairs for Group-Invariant Hermitian Polynomials

We study the signature pair for certain group-invariant Hermitian polynomials arising in CR geometry. In particular, we determine the signature pair for the finite subgroups of $SU(2)$. We introduce the asymptotic positivity ratio and compute it for cyclic subgroups of $U(2)$. We calculate the signature pair for dihedral subgroups of $U(2)$.