I. G. Macdonald – författare

This is a new and much expanded edition of Professor Macdonald's acclaimed monograph on Symmetric Functions and Hall Polynomials. Almost every chapter has new sections and many new examples have been included throughout. In addition there are two new chapters (6 and 7).Chapter 6 contains an extended account of a family of symmetric functions depending on two parameters. These symmetric functions include as particular cases many of those encountered earlier in the book and they also include, as a limiting case, Jack's symmetric functions depending on a parameter α. Many of the properties of the Schur functions generalize to these two-parameter symmetric functions.Chapter 7 is devoted to the study of the zxonal polynomials, long familiar to staticians. From one point of view, they are a special case of Jack's symmetric functions (the parameter α being equal to 2) but their combinatorial and group-theoretic connections make them worthy of study in their own right.

This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials.The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st centuryMacdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and so on. Macdonald polynomials have become a part of basic material that a researcher simply must know if (s)he wants to work in one of the above domains, ensuring this new edition will appeal to a very broad mathematical audience.Featuring a new foreword by Professor Richard Stanley of MIT.

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.