Symmetric Functions and Orthogonal Polynomials PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Symmetric Functions and Orthogonal Polynomials PDF full book. Access full book title Symmetric Functions and Orthogonal Polynomials by Ian Grant Macdonald. Download full books in PDF and EPUB format.
Author: Ian Grant Macdonald
Publisher: American Mathematical Soc.
ISBN: 0821807706
Category : Mathematics
Languages : en
Pages : 71
Get Book Here
Book Description
One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.
Author: Ian Grant Macdonald
Publisher: American Mathematical Soc.
ISBN: 0821807706
Category : Mathematics
Languages : en
Pages : 71
Get Book Here
Book Description
One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.
Author: Alain Lascoux
Publisher: American Mathematical Soc.
ISBN: 0821828711
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
Book Description
The theory of symmetric functions is an old topic in mathematics, which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and its occurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods, or the method of Cauchy and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.
Author: Ian Grant Macdonald
Publisher: Oxford University Press
ISBN: 9780198504504
Category : Mathematics
Languages : en
Pages : 496
Get Book Here
Book 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.
Author: Taekyun Kim
Publisher: MDPI
ISBN: 3036503609
Category : Mathematics
Languages : en
Pages : 206
Get Book Here
Book Description
The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.
Author: Gabor Szeg
Publisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 448
Get Book Here
Book Description
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
Author: William Jones
Publisher: CRC Press
ISBN: 1000153673
Category : Mathematics
Languages : en
Pages : 442
Get Book Here
Book Description
"Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."
Author: I. G. Macdonald
Publisher: Cambridge University Press
ISBN: 9780521824729
Category : Mathematics
Languages : en
Pages : 200
Get Book Here
Book Description
First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Author: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
Get Book Here
Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521789882
Category : Mathematics
Languages : en
Pages : 684
Get Book Here
Book Description
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Author: Richard Beals
Publisher: Cambridge University Press
ISBN: 1107106982
Category : Mathematics
Languages : en
Pages : 489
Get Book Here
Book Description
A comprehensive graduate-level introduction to classical and contemporary aspects of special functions.
