Symmetric Functions and Hall Polynomials by I.G. Macdonald (English) Paperback B

Description: Symmetric Functions and Hall Polynomials by I.G. Macdonald This second edition updates and expands the acclaimed first edition, adding a new chapter on a family of symmetric functions depending rationally on two parameters and also a chapter on zonal polynomials. It is available for the first time in paperback. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This is a paperback version of the second, much expanded, edition of Professor Macdonalds acclaimed monograph on symmetric functions and Hall polynomials. Almost every chapter has new sections and new examples have been included throughout. Extra material in the appendix to Chapter 1, for example, includes an account of the related theory of polynomial representations of the general linear groups (always in characteristic zero). Chapters 6 and 7 are new to thesecond edition: Chapter 6 contains an extended account of a family of symmetric functions depending rationally on two parameters. These symmetric functions include as particular cases many of thoseencountered earlier in the book but they also include, as a limiting case, Jacks symmetric functions depending on a parameter (Many of the properties of the Schur functions generalize to these two-parameter symmetric functions, but the proofs (at present) are usually more elaborate. Chapter 7 is devoted to the study of the zonal polynomials, long familiar to statisticians. From one point of view they are a special case of Jacks symmetric functions (the parameter ( being equal to 2) but theircombinatorial and group-theoretic connections make them worthy of study in their own right. From reviews of the first edition: Despite the amount of material of such greatpotential 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 ...In addition to providing a self-contained and coherent account of well-known andclassical work, there is a great deal which is original. The book is dotted with gems, both old and new...It is a substantial and valuable volume and will be regarded as the authoritative source which has been long awaited in thissubject. LMS book reviews From reviews of the second edition: Evidently this second edition will be the source and reference book for symmetric functions in the near future. bl. Math. Author Biography Professor Ian Grant Macdonald, Emeritus Professor, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London, E1 4NS. Tel: 0171 975 5514; fax: 0181 981 9587. Professor Macdonald is a series editor for the Oxford Mathematical Monographs series, and is a key speaker at the International Congress of Mathematicians 1998. Table of Contents I. Symmetric functionsII. Hall polynomialsIII. HallLittlewood symmetric functionsIV. The characters of GLn over a finite fieldV. The Hecke ring of GLn over a finite fieldVI. Symmetric functions with two parametersVII. Zonal polynomials Review From reviews of the second edition:`Evidently this second edition will be the source and reference book for symmetric functions in the next future.Zentralblatt fÜr Mathematik Long Description This is a paperback version of the second, much expanded, edition of Professor Macdonalds acclaimed monograph on symmetric functions and Hall polynomials. Almost every chapter has new sections and new examples have been included throughout. Extra material in the appendix to Chapter 1, for example, includes an account of the related theory of polynomial representations of the general linear groups (always in characteristic zero). Chapters 6 and 7 are new to thesecond edition: Chapter 6 contains an extended account of a family of symmetric functions depending rationally on two parameters. These symmetric functions include as particular cases many of thoseencountered earlier in the book but they also include, as a limiting case, Jacks symmetric functions depending on a parameter (Many of the properties of the Schur functions generalize to these two-parameter symmetric functions, but the proofs (at present) are usually more elaborate. Chapter 7 is devoted to the study of the zonal polynomials, long familiar to statisticians. From one point of view they are a special case of Jacks symmetric functions (the parameter ( being equal to 2) but theircombinatorial and group-theoretic connections make them worthy of study in their own right. From reviews of the first edition: Despite the amount of material of such greatpotential 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 ...In addition to providing a self-contained and coherent account of well-known andclassical work, there is a great deal which is original. The book is dotted with gems, both old and new...It is a substantial and valuable volume and will be regarded as the authoritative source which has been long awaited in thissubject. LMS book reviews From reviews of the second edition: Evidently this second edition will be the source and reference book for symmetric functions in the near future. bl. Math. Review Text From reviews of the second edition:`Evidently this second edition will be the source and reference book for symmetric functions in the next future.Zentralblatt fÜr Mathematik Review Quote "This new edition incorporates the additions to the translated version, as well as a tremendous amount of new material . . . . Readers familiar with the first edition will find that the authors uniquely brief but lucid style has not changed . . . . This masterful new edition will undoubtedly remain the standard reference for symmetric polynomials. It serves as proof of the metatheorem that wherever natural structures indexed by partitions arise, the algebra of symmetric functions is nearby."--Mathematical Reviews Promotional "Headline" 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 Feature Available for first time in paperbackOnly book on this important subject Details ISBN0198504500 Pages 488 Series Oxford Mathematical Monographs Language English Edition 2nd ISBN-10 0198504500 ISBN-13 9780198504504 Media Book Format Paperback Imprint Oxford University Press Place of Publication Oxford Country of Publication United Kingdom DEWEY 515.55 Short Title OXFORD MATHEMATICAL MONOGRAPHS Illustrations black & white illustrations DOI 10.1604/9780198504504 UK Release Date 1998-07-09 AU Release Date 1998-07-09 NZ Release Date 1998-07-09 Author I.G. Macdonald Publisher Oxford University Press Edition Description 2nd Revised edition Year 1998 Publication Date 1998-07-09 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. 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