GRADED CONTRACTIONS OF REPRESENTATIONS OF SPECIAL LINEAR LIE-ALGEBRASWITH RESPECT TO THEIR MAXIMAL PARABOLIC SUBALGEBRAS

Parabolic gradings of the classical simple Lie algebras sl(N, C) (N gr eater-than-or-equal-to 3) are described for all maximal parabolic suba lgebras. All contractions are found which leave a maximal parabolic su balgebra intact and which preserve a parabolic grading (parabolic cont ractions of Lie algebras). Contractions of the irreducible representat ions of sl(N, C) for each parabolic contraction of the Lie algebra are the main results of the article.