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Representation of Lie Groups and Special Functions

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  • Book
  • © 1995

Overview

Authors:
  1. N. Ja. Vilenkin

    1. The Correspondence Pedagogical Institute, Moscow, Russia

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  2. A. U. Klimyk

    1. Institute for Theoretical Physics, Ukrainian Academy of Sciences, Kiev, Ukraine

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 316)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xvi
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  2. h-Harmonic Polynomials, h-Hankel Transform, and Coxeter Groups

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 1-66

  3. Symmetric Polynomials and Symmetric Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 67-184

  4. Hypergeometric Functions Related to Jack Polynomials

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 185-264

  5. Clebsch-Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 265-316

  6. Clebsch-Gordan Coefficients of the group U(n) and Related Generalizations of Hypergeometric Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 317-392

  7. Gel’fand Hypergeometric Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 393-462

  8. Back Matter

    Pages 463-504
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Keywords

About this book

In 1991-1993 our three-volume book "Representation of Lie Groups and Spe­ cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep­ resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza­ tions of classical special functions that were dictated by matrix elements of repre­ sentations.

Authors and Affiliations

  • The Correspondence Pedagogical Institute, Moscow, Russia

    N. Ja. Vilenkin

  • Institute for Theoretical Physics, Ukrainian Academy of Sciences, Kiev, Ukraine

    A. U. Klimyk

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