Abstract
Parabolic gradings of the classical simple Lie algebras sl(N,C) (N>or=3) are described for all maximal parabolic subalgebras. All contractions are found which leave a maximal parabolic subalgebra intact and which preserve a parabolic grading (parabolic contractions of Lie algebras). Contractions of the irreducible representations of sl(N,C) for each parabolic contraction of the Lie algebra are the main results of the article.
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