DJKM algebras and non-classical orthogonal polynomials

We describe families of polynomials arising in the study of the universal central extensions of Lie algebras introduced by Date, Jimbo, Kashiwara, and Miwa (1983) [6] in their work on the Landau–Lifshitz equations. We show these two families of polynomials satisfy certain fourth order linear differential equations by direct computation and one of the families is a particular collection of associated ultraspherical polynomials.