Author: Carol H. ChangPublisher:
ISBN:
Category :
Languages : en
Pages : 208
Book Description
Geometric Interpretations of the Macdonald Polynomials and the N! Conjecture
Author: Carol H. ChangThe $q,t$-Catalan Numbers and the Space of Diagonal Harmonics
Author: James HaglundPublisher: American Mathematical Soc.
ISBN: 0821844113
Category : Mathematics
Languages : en
Pages : 178
Book Description
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
Combinatorics of Macdonald Polynomials and Extensions
Author: Jason BandlowPublisher:
ISBN: 9781109968903
Category :
Languages : en
Pages : 80
Book Description
In 2003, Jim Haglund proposed a purely combinatorial description of the Macdonald polynomials. This description, the generating function for a particular pair of statistics, was soon proved correct by Haiman, Haglund and Nick Loehr.
Affine Hecke Algebras and Orthogonal Polynomials
Author: I. G. MacdonaldPublisher: Cambridge University Press
ISBN: 9780521824729
Category : Mathematics
Languages : en
Pages : 200
Book Description
First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Symmetric Functions and Hall Polynomials
Author: Ian Grant MacdonaldPublisher: Oxford University Press
ISBN: 9780198504504
Category : Mathematics
Languages : en
Pages : 496
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.
The Symmetric Group
Author: Bruce E. SaganPublisher: Springer Science & Business Media
ISBN: 1475768044
Category : Mathematics
Languages : en
Pages : 254
Book Description
This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH
Perspectives in Representation Theory
Author: Pavel EtingofPublisher: American Mathematical Soc.
ISBN: 0821891707
Category : Mathematics
Languages : en
Pages : 384
Book Description
This volume contains the proceedings of the conference Perspectives in Representation Theory, held from May 12-17, 2012, at Yale University, in honor of Igor Frenkel's 60th birthday. The aim of the conference was to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and -adic groups, and quantum gauge theories. The papers in this volume present representation theory connections to numerous other subjects, as well as some of the most recent advances in representation theory, including those which occurred thanks to the application of techniques in other areas of mathematics, and of ideas of quantum field theory and string theory.
New Perspectives in Algebraic Combinatorics
Author: Louis J. BilleraPublisher: Cambridge University Press
ISBN: 9780521770873
Category : Mathematics
Languages : en
Pages : 360
Book Description
This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.
Double Affine Hecke Algebras
Author: Ivan CherednikPublisher: Cambridge University Press
ISBN: 0521609186
Category : Mathematics
Languages : en
Pages : 449
Book Description
This is an essentially self-contained monograph centered on the new double Hecke algebra technique.
George E. Andrews 80 Years of Combinatory Analysis
Author: Krishnaswami AlladiPublisher: Springer Nature
ISBN: 3030570509
Category : Mathematics
Languages : en
Pages : 810
Book Description
This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.