Wigner's $D$-matrix elements for $SU(3)$ - A Generating Function Approach

TL;DR

This paper derives a generating function for Wigner's D-matrix elements of SU(3), enabling explicit closed-form expressions for individual matrix elements, advancing computational methods in representation theory.

Contribution

It introduces a novel generating function approach to derive explicit formulas for SU(3) Wigner D-matrix elements, which was not previously available.

Findings

Explicit closed-form expressions for SU(3) Wigner D-matrix elements.

A new generating function for these matrix elements.

Enhanced computational techniques for SU(3) representations.

Abstract

A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.