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

TL;DR

This paper explores eigenvalue problems in $rak{su}(2)$ models, revealing biorthogonality relations of Krawtchouk polynomial generating functions and connecting these findings to Padé approximation.

Contribution

It clarifies biorthogonality relations in $rak{su}(2)$ models and links them to Padé approximation, advancing understanding of polynomial generating functions in quantum algebra.

Findings

Biorthogonality relations between generating functions are established.

Connections between Krawtchouk polynomials and Padé approximation are demonstrated.

Eigenvalue problems are analyzed across multiple models.

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.