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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 century
Macdonald 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.
List of contents
- I. Symmetric functions
- II. Hall polynomials
- III. HallLittlewood symmetric functions
- IV. The characters of GLn over a finite field
- V. The Hecke ring of GLn over a finite field
- VI. Symmetric functions with two parameters
- VII. Zonal polynomials
About the author
I. G. Macdonald, Emeritus Professor, Queen Mary and Westfield College, London
Summary
Reissued in the Oxford Classical Texts, this acclaimed second edition is nowadays the key resource on Macdonald polynomials, important for many research mathematicians.
Additional text
From reviews of the second edition: 'Evidently this second edition will be the source and reference book for symmetric functions in the near future.
Report
From reviews of the first edition: 'Despite the amount of material of such great potential interest to mathematicians...the theory of symmetric functions remains all but unknown to the persons it is most likely to benefit...Hopefully this beautifully written book will put an end to this state of affairs...I have no doubt that this book will become the definitive reference on symmetric functions and their applications.' Bulletin of the AMS
