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 gre ater 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 subal gebras. All contractions which leave a maximal parabolic subalgebra in tact and which preserve a parabolic grading (parabolic contractions of Lie algebras) are found. Contractions of the irreducible representati ons for each parabolic contraction of the Lie algebra are the main res ults of the article.