In this paper, we describe a compact and practical algorithm to construct Hermitian Young projection operators for irreducible representations of the special unitary group and discuss why ordinary non-Hermitian Young projection operators are unsuitable for physics applications. The proof of this construction algorithm uses the iterative method described by Keppeler and Sjödahl [J. Math. Phys. 55, 021702 (2014)]. We further show that Hermitian Young projection operators share desirable properties with Young tableaux, namely, a nested hierarchy when “adding a particle.” We close by exhibiting the enormous advantage of the Hermitian Young projection operators constructed in this paper over those given by Keppeler and Sjödahl.
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