A note on $\mathfrak{su}(2)$ models and the biorthogonality of generating functions of Krawtchouk polynomials

Abstract

Eigenvalue problems on irreducible $\mathfrak{su}(2)$ modules and their adjoints are considered in the Bargmann, Barut-Girardello and finite difference models. The biorthogonality relations that arise between the corresponding generating functions of the Krawtchouk polynomials are sorted out. A link with Pad\'e approximation is made.