The generating function for a particular class of characters of SU(n)

TL;DR

This paper derives a rational determinantal generating function for a specific subset of SU(n) characters, characterized by Young diagrams with two equal rows, expressed via Schur polynomials.

Contribution

It provides a novel explicit formula for the generating function of certain SU(n) characters with a specific Young diagram shape, using determinantal and Schur polynomial techniques.

Findings

Derived a rational determinantal expression for the generating function

Expressed the result in terms of Schur polynomials

Focused on characters with Young diagrams having two equal rows

Abstract

We compute the generating function for the characters of the irreducible representations of SU(n) whose associated Young diagrams have only two rows with the same number of boxes. The result is a rational determinantal expression in which both the numerator and the denominator have a simple structure when expressed in terms of Schur polynomials.