GRADED CONTRACTIONS OF REPRESENTATIONS OF ORTHOGONAL AND SYMPLECTIC LIE-ALGEBRAS WITH RESPECT TO THEIR MAXIMAL PARABOLIC SUBALGEBRAS

Parabolic gradings of the classical simple Lie algebras o(N,C), (N greater than or equal to 5) and sp(2n, C), (n greater than or equal to 2) with complex parameters are described for all maximal parabolic subalgebras. All contractions which leave a maximal parabolic subalgebra intact and which preserve a parabolic grading (parabolic contractions of Lie algebras) are found. Contractions of the irreducible representations for each parabolic contraction of the Lie algebra are the main results of the article.