Orthogonal Polynomials, a Szegő--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere

Connor J. Gauntlett, David P. Kimsey

We introduce a theory of orthogonal polynomials on the unit sphere of the quaternions based on the notion of a $q$-positive measure (which originated in a work of Alpay, Colombo, t…