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We generalize the famous weight basis constructions of the finite-dimensionalirreducible representations of $\mathfrak{sl}(n,\mathbb{C})$ obtained byGelfand and Tsetlin in 1950. Using combinatorial methods, we construct one suchbasis for each finite-dimensional representation of$\mathfrak{sl}(n,\mathbb{C})$ associated to a given skew Schur function. Ourconstructions use diamond-colored distributive lattices of skew-shapedsemistandard tableaux that generalize some classical Gelfand--Tsetlin (GT)lattices. Our constructions take place within the context of a certainprogrammatic study of poset models for semisimple Lie algebra representationsand Weyl group symmetric functions undertaken by the first-named author andothers. Some key aspects of the methodology of that program are recapitulatedhere. Combinatorial and representation-theoretic applications of ourconstructions are pursued here and elsewhere.

Gelfand--Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions