Orthogonalization and polarization of Yangians

A new realization of the Yangian of [Formula: see text] is defined for any family of orthogonal polynomials. We show that the new choice of generators satisfies the RTT relation in the case of Dickson polynomials. Similar construction can be made for any family of functions satisfying certain recurrence relations, e.g. [Formula: see text]-Pochhammer symbols and Bessel functions. Furthermore, using an analog of the Jordan–Schwinger map, we introduce the ternary Yangian for a certain ternary extension of a given Lie algebra as a flat deformation of its current algebra.