Kravchuk and Meixner polynomials of a discrete variable and irreducible representations of the Lie groups SO(3) and SO(2,1)

Resumen:

The study of Lie algebra and group irreducible representations has traditionally considered their action on functions of a continuous manifold (e.g. the `rotation' Lie algebra so(3) on functions on the sphere). We show that functions of a discrete variable, which are not well known in the main stream literature, are on equal footing for that study in the case of low-dimensional Lie algebras and groups. In particular, Kravchuk functions are actually `encoded' within finite-dimensional irreducible unitary representations of the group SO(3), whereas Meixner functions are associated with infinite-dimensional irreducible unitary representations of the three-dimensional Lorentz group SO(2,1).