In 1991-1993 our three-volume e-book "Representation of Lie teams and Spe cial features" used to be released. after we began to write that e-book (in 1983), editors of "Kluwer educational Publishers" expressed their want for the publication to be of encyclopaedic kind at the topic. Interrelations among representations of Lie teams and designated capabilities are very large. This width could be defined through life of alternative forms of Lie teams and through richness of the idea in their rep resentations. this is because the e-book, pointed out above, unfold to 3 substantial volumes. impression of representations of Lie teams and Lie algebras upon the speculation of specified services is lasting. This concept is constructing extra and strategies of the illustration idea are of significant significance during this improvement. while the ebook "Representation of Lie teams and specific capabilities" ,vol. 1-3, was once below guidance, new instructions of the speculation of particular capabilities, attached with workforce representations, seemed. New vital effects have been came upon within the conventional instructions. This impelled us to write down a continuation of our three-volume publication on courting among representations and designated features. the results of our additional paintings is the current ebook. The three-volume ebook, released ahead of, used to be committed customarily to learning classical certain services and orthogonal polynomials by way of matrix components, Clebsch-Gordan and Racah coefficients of team representations and to generaliza tions of classical distinct features that have been dictated through matrix components of repre sentations.
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