Representations of SU(2) and Jacobi polynomials

TL;DR

This paper provides a tutorial on SU(2) representation theory, highlighting how Jacobi polynomials appear in matrix elements, and explores the historical development of this mathematical connection.

Contribution

It offers a comprehensive introduction to SU(2) representations with a focus on Jacobi polynomials, including historical context and mathematical details.

Findings

Jacobi polynomials naturally arise in SU(2) matrix elements

Historical insights into the connection between SU(2) and Jacobi polynomials

Tutorial exposition clarifies the role of special functions in representation theory

Abstract

This is a tutorial introduction to the representation theory of SU(2) with emphasis on the occurrence of Jacobi polynomials in the matrix elements of the irreducible representations. The last section traces the history of the insight that Jacobi polynomials occur in the representation theory of SU(2).