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Jack, Hall-Littlewood and Macdonald polynomials. Workshop on Jack, Hall-Littlewood and Macdonald polynomials, ICMS, Edinburgh, UK, September 23–26, 2003. (English) Zbl 1102.33001
Contemporary Mathematics 417. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3683-8/pbk). xix, 360 p. $ 79.00 (2006).

The articles of this volume will be reviewed individually.

The subject of symmetric functions began with the work of Jacobi, Schur, Weyl, Young and others on the Schur polynomials. In the 1950’s and 60’s, far-reaching generalizations of Schur polynomials were obtained by Hall and Littlewood (independently) and, in a different direction, by Jack. In the 1980’s, Macdonald unified these developments by introducing a family of polynomials associated with arbitrary root systems.

The last twenty years have witnessed considerable progress in this area, revealing new and profound connections with representation theory, algebraic geometry, combinatorics, special functions, classical analysis and mathematical physics. All these fields and more are represented in this volume, which contains the proceedings of a conference on “Jack, Hall-Littlewood and Macdonald polynomials” held at ICMS, Edinburgh, during September 23-26, 2003.

In addition to new results by leading researchers, the book contains a wealth of historical material, including brief biographies of Hall, Littlewood, Jack and Macdonald; the original papers of Littlewood and Jack; notes on Hall’s work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald). The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.

MSC:
33-06Proceedings of conferences (special functions)
00B25Proceedings of conferences of miscellaneous specific interest
33D52Basic orthogonal polynomials and functions associated with root systems
33D80Connections of basic hypergeometric functions with groups, algebras and related topics
33D45Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33D67Basic hypergeometric functions associated with root systems