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We construct new families of vector orthogonal polynomials that have theproperty to be eigenfunctions of some differential operator. They areextensions of the Hermite and Laguerre polynomial systems. A third family,whose first member has been found by Y. Ben Cheikh and K. Douak is alsoconstructed. The ideas behind our approach lie in the studies of bispectraloperators. We exploit automorphisms of associative algebras which transformelementary vector orthogonal polynomial systems which are eigenfunctions of adifferential operator into other systems of this type.

Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials