Algebraic properties of Kaneko-Zagier lifts of supersingular polynomials

studied lifts to \mathbf {Q}[x]. Among these is one introduced by Kaneko and Zagier, which, when interpreted as a specialized Jacobi polynomial, is seen to coincide with a lift discovered by Brillhart and Morton a few years later. The algebraic properties of this family of lifts of \mathfrak{S}_\ell (x) are not well-understood. We focus on a conjecture of Mahlburg and Ono regarding the maximality of their Galois groups (when shorn of their trivial linear factors) and also establish their irreducibility in some previously unknown cases.]]>