Symmetric Functions and Hall Polynomials

Book excerpt: 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.