{"title":"I G Macdonald","description":null,"products":[{"product_id":"symmetric-functions-and-hall-polynomials-book-i-g-macdonald-9780198739128","title":"Symmetric Functions and Hall Polynomials","description":"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.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50423088087313,"sku":"CIN0198739125G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50627780903185,"sku":"GOR009024283","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0198739125.jpg?v=1750812073"},{"product_id":"affine-hecke-algebras-and-orthogonal-polynomials-book-i-g-macdonald-9780521824729","title":"Affine Hecke Algebras and Orthogonal Polynomials","description":"In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the Askey-Wilson polynomials, which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This book, first published in 2003, is a comprehensive and organised account of the subject aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is an essentially self-contained treatment, accessible to graduate students familiar with root systems and Weyl groups. The first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51003261288721,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51003263942929,"sku":"NIN9780521824729","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52662426829073,"sku":"NLS9780521824729","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":53088676249873,"sku":"NGR9780521824729","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521824729.jpg?v=1751166459"},{"product_id":"symmetric-functions-and-hall-polynomials-book-i-g-macdonald-9780198535300","title":"Symmetric Functions and Hall Polynomials","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51460326981905,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51460327309585,"sku":"GOR014288888","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0198535309.jpg?v=1751132337"},{"product_id":"symmetric-functions-and-hall-polynomials-book-i-g-macdonald-9780198504504","title":"Symmetric Functions and Hall Polynomials","description":"This is a paperback version of the second, much expanded, edition of Professor Macdonald's 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 the second 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 those encountered earlier in the book but they also include, as a limiting case, Jack's 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 Jack's symmetric functions (the parameter ( being equal to 2) but their combinatorial 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 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 '...In addition to providing a self-contained and coherent account of well-known and classical 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 this subject.' 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.'Zbl. Math.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52151244685585,"sku":"NLS9780198504504","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52858122666257,"sku":"NIN9780198504504","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780198504504.jpg?v=1757612683"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-i-g-macdonald.oembed","provider":"World of Books ","version":"1.0","type":"link"}