Para-orthogonal polynomials from constant Verblunsky coefficients

Orthogonal polynomials on the unit circle associated with constant Verblunsky coefficients are also known as Geronimus polynomials. We consider the properties of some special sequences of para-orthogonal polynomials that follow from the Geronimus polynomials and, as applications, obtain information concerning certain associated quadrature rules and also other related orthogonal polynomials. Positive chain sequences play an important role in our study.