The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces

摘要

The main aim of this paper is to construct explicitly orthogonal bases for the spaces H ~k _s(? ~m) of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space ? ~m, which take values in the space of s-vectors. Actually, we describe even the so-called Gelfand-Tsetlin bases for such spaces in terms of Gegenbauer polynomials. As an application, we obtain an algorithm on how to compute an orthogonal basis of the space of homogeneous solutions for an arbitrary generalized Moisil-Théodoresco system in ? ~m.