Representation of Lie Groups and Special Functions: Recent Advances

Representation of Lie Groups and Special Functions

by Naum Yakovlevich Vilenkin, A.U. Klimyk

The present book is a continuation of the three-volume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to Clebsch-Gordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics.

524 pages, Kindle Edition

First published November 30, 1994

About the author

Naum Yakovlevich Vilenkin (Russian: Наум Яковлевич Виленкин, October 30, 1920 in Moscow – October 19, 1991 in Moscow) was a Soviet mathematician, an expert in representation theory, the theory of special functions, functional analysis, and combinatorics. He is best known as the author of many books in recreational mathematics aimed at middle and high school students.