The generalized Alexander polynomial is an invariant of virtual knots/links up to factors of +/- s and t, as described by Louis Kauffman and David E. Radford in Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links, arXiv:math.GT/0112280.
Under inversion and horizontal mirror images, s goes to s-1 and t goes to t-1. Under vertical mirror images, s goes to t and t goes to s.