Spherical monogenics in dimension 3 and discrete orthogonal polynomials

In this educational talk, my main goal is to show how a family of discrete orthogonal polynomials from the Askey scheme naturally arises in the study of spherical monogenics in dimension 3.
This connection will be revealed by making explicit the action of the so(3) Lie algebra that preserves the monogenics on a basis constructed using a tower of CK extensions.
It will then be shown that different towers of CK extensions lead to different orthogonal bases. The expansion coefficients between two such bases are subsequently expressed using the Krawtchouk discrete orthogonal polynomials.