Jack, Hall-Littlewood and Macdonald Polynomials
Author:
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 360
ISBN-13: 9780821857472
DOWNLOAD EBOOKRead and Download eBook Full
Author:
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 360
ISBN-13: 9780821857472
DOWNLOAD EBOOKAuthor: Vadim B. Kuznetsov
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 386
ISBN-13: 0821836838
DOWNLOAD EBOOKThe subject of symmetric functions began with the work of Jacobi, Schur, Weyl, Young and others on the Schur polynomials. In the 1950's and 60's, far-reaching generalizations of Schur polynomials were obtained by Hall and Littlewood (independently) and, in a different direction, by Jack. In the 1980's, Macdonald unified these developments by introducing a family of polynomials associated with arbitrary root systems. The last twenty years have witnessed considerable progress in this area, revealing new and profound connections with representation theory, algebraic geometry, combinatorics, special functions, classical analysis and mathematical physics. All these fields and more are represented in this volume, which contains the proceedings of a conference on Jack, Hall-Littlewood and Macdonald polynomials held at ICMS, Edinburgh, during September 23-26, 2003. of historical material, including brief biographies of Hall, Littlewood, Jack and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald). The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.
Author: Masatoshi Noumi
Publisher: Springer Nature
Published:
Total Pages: 137
ISBN-13: 9819945879
DOWNLOAD EBOOKAuthor: Ian Grant Macdonald
Publisher: Oxford University Press
Published: 1998
Total Pages: 496
ISBN-13: 9780198504504
DOWNLOAD EBOOKThis 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: James Haglund
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 178
ISBN-13: 0821844113
DOWNLOAD EBOOKThis 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.
Author: Yusra Fatima Naqvi
Publisher:
Published: 2014
Total Pages: 50
ISBN-13:
DOWNLOAD EBOOKJack polynomials generalize several classical families of symmetric polynomials, including Schur polynomials, and are further generalized by Macdonald polynomials. In 1989, Richard Stanley conjectured that if the Littlewood-Richardson coefficient for a triple of Schur polynomials is 1, then the corresponding coefficient for Jack polynomials can be expressed as a product of weighted hooks of the Young diagrams associated to the partitions indexing the coefficient. We prove a special case of this conjecture in which the partitions indexing the Littlewood-Richardson coefficient have at most 3 parts. We also show that this result extends to Macdonald polynomials.
Author: Inka Klostermann
Publisher:
Published: 2011
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKAuthor: Fabio Ancona
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 416
ISBN-13: 0821837664
DOWNLOAD EBOOKWhile rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperb These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. in addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. in all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.
Author: Lothar Gerritzen
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 190
ISBN-13: 0821840371
DOWNLOAD EBOOKThe book consists of contributions related mostly to public-key cryptography, including the design of new cryptographic primitives as well as cryptanalysis of previously suggested schemes. Most papers are original research papers in the area that can be loosely defined as ``non-commutative cryptography''; this means that groups (or other algebraic structures) which are used as platforms are non-commutative.