Signature Pairs for Group-Invariant Hermitian Polynomials

TL;DR

This paper investigates the signature pairs of group-invariant Hermitian polynomials in CR geometry, providing explicit calculations for various finite subgroups of SU(2) and U(2), and introduces an asymptotic positivity ratio.

Contribution

It determines the signature pairs for finite subgroups of SU(2) and computes the asymptotic positivity ratio for cyclic subgroups of U(2), advancing understanding of group-invariant polynomials.

Findings

Signature pairs for finite subgroups of SU(2) determined

Asymptotic positivity ratio computed for cyclic subgroups of U(2)

Signature pairs for dihedral subgroups of U(2) calculated

Abstract

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 $U(2)$.