Ebook: Representation of Lie Groups and Special Functions: Recent Advances

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.

---

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.

---

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.
Content:
Front Matter....Pages i-xvi
h-Harmonic Polynomials, h-Hankel Transform, and Coxeter Groups....Pages 1-66
Symmetric Polynomials and Symmetric Functions....Pages 67-184
Hypergeometric Functions Related to Jack Polynomials....Pages 185-264
Clebsch-Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations....Pages 265-316
Clebsch-Gordan Coefficients of the group U(n) and Related Generalizations of Hypergeometric Functions....Pages 317-392
Gel’fand Hypergeometric Functions....Pages 393-462
Back Matter....Pages 463-504

---

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.
Content:
Front Matter....Pages i-xvi
h-Harmonic Polynomials, h-Hankel Transform, and Coxeter Groups....Pages 1-66
Symmetric Polynomials and Symmetric Functions....Pages 67-184
Hypergeometric Functions Related to Jack Polynomials....Pages 185-264
Clebsch-Gordan Coefficients and Racah Coefficients of Finite Dimensional Representations....Pages 265-316
Clebsch-Gordan Coefficients of the group U(n) and Related Generalizations of Hypergeometric Functions....Pages 317-392
Gel’fand Hypergeometric Functions....Pages 393-462
Back Matter....Pages 463-504
....