Compact Hermitian Young Projection Operators

TL;DR

This paper introduces a compact, practical algorithm for constructing Hermitian Young projection operators for SU(N), improving their usability in physics by ensuring desirable properties and demonstrating significant advantages over previous methods.

Contribution

The paper presents a new, efficient algorithm for Hermitian Young projection operators that are better suited for physics applications than traditional Young operators.

Findings

Hermitian Young projection operators have a nested hierarchy property.

The new construction is more compact and practical.

Demonstrates clear advantages over previous methods by Keppeler and Sj"odahl.

Abstract

In this paper, we describe a compact and practical algorithm to construct Hermitian Young projection operators for irreducible representations of the special unitary group SU(N), and discuss why ordinary Young projection operators are unsuitable for physics applications. The proof of this construction algorithm uses the iterative method described by Keppeler and Sj\"odahl. We further show that Hermitian Young projection operators share desirable properties with Young tableaux, namely a nested hierarchy when "adding a particle". We end by exhibiting the enormous advantage of the Hermitian Young projection operators constructed in this paper over those given by Keppeler and Sj\"odahl.