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Author :
Publisher :
ISBN 13 :
Total Pages : 4 pages
Book Rating : 4.:/5 (923 download)
Download or read book Quantum Double Schubert Polynomials written by and published by . This book was released on 1997 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Laurent Manivel
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821541
Total Pages : 180 pages
Book Rating : 4.8/5 (215 download)
Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel and published by American Mathematical Soc.. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.
Author : William Fulton
Publisher : Springer
ISBN 13 : 3540698043
Total Pages : 158 pages
Book Rating : 4.5/5 (46 download)
Download or read book Schubert Varieties and Degeneracy Loci written by William Fulton and published by Springer. This book was released on 2006-11-13 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.
Author : Jan Felipe Van Diejen
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873298
Total Pages : 302 pages
Book Rating : 4.8/5 (732 download)
Download or read book Algebraic Methods and Q-special Functions written by Jan Felipe Van Diejen and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.
Author : Sara C. Billey
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.:/5 (318 download)
Download or read book An Abstract Definition of Schubert Polynomials Extending to the Classical Groups written by Sara C. Billey and published by . This book was released on 1994 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin A. Guest
Publisher : OUP Oxford
ISBN 13 : 0191606960
Total Pages : 336 pages
Book Rating : 4.1/5 (916 download)
Download or read book From Quantum Cohomology to Integrable Systems written by Martin A. Guest and published by OUP Oxford. This book was released on 2008-03-13 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.
Author : Ian Grant Macdonald
Publisher : Dép. de mathématique et d'informatique, Université du Québec à Montréal
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.3/5 (91 download)
Download or read book Notes on Schubert Polynomials written by Ian Grant Macdonald and published by Dép. de mathématique et d'informatique, Université du Québec à Montréal. This book was released on 1991 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I︠U︡. I. Manin
Publisher : American Mathematical Soc.
ISBN 13 : 0821819178
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)
Download or read book Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces written by I︠U︡. I. Manin and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the construction of quantum cohomology and reviews the algebraic geometry mechanisms involved in this construction (intersection and deformation theory of Deligne-Artin and Mumford stacks). Yuri Manin is currently the director of the Max-Planck-Institut für Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and almost 200 research articles in algebraic geometry, number theory, mathematical physics, history of culture, and psycholinguistics. Manin's books, such as Cubic Forms: Algebra, Geometry, and Arithmetic (1974), A Course in Mathematical Logic (1977), Gauge Field Theory and Complex Geometry (1988), Elementary Particles: Mathematics, Physics and Philosophy (1989, with I. Yu. Kobzarev), Topics in Non-commutative Geometry (1991), and Methods of Homological Algebra (1996, with S. I. Gelfand), secured for him solid recognition as an excellent expositor. Undoubtedly the present book will serve mathematicians for many years to come.
Author : Thomas Lam
Publisher : Springer
ISBN 13 : 1493906828
Total Pages : 226 pages
Book Rating : 4.4/5 (939 download)
Download or read book k-Schur Functions and Affine Schubert Calculus written by Thomas Lam and published by Springer. This book was released on 2014-06-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
Author : Alain Lascoux
Publisher : American Mathematical Soc.
ISBN 13 : 0821828711
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)
Download or read book Symmetric Functions and Combinatorial Operators on Polynomials written by Alain Lascoux and published by American Mathematical Soc.. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 0306483734
Total Pages : 564 pages
Book Rating : 4.3/5 (64 download)
Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Author : Avinash J. Dalal
Publisher :
ISBN 13 :
Total Pages : 238 pages
Book Rating : 4.:/5 (885 download)
Download or read book Quantum and Affine Schubert Calculus and Macdonald Polynomials written by Avinash J. Dalal and published by . This book was released on 2014 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is on the theory of symmetric functions and quantum and affine Schubert calculus. Namely, it establishes that the theory of symmetric Macdonald polynomials aligns with quantum and affine Schubert calculus using a discovery that distinguished weak chains can be identified by chains in the strong (Bruhat) order poset on the type-A affine Weyl group. Through this discovery, there is a construction of two one-parameter families of functions that respectively transition positively with Hall-Littlewood polynomials and Macdonald's P-functions. Furthermore, these functions specialize to the representatives for Schubert classes of homology and cohomology of the affine Grassmannian. This shows that the theory of symmetric Macdonald polynomials connects with affine Schubert calculus. There is a generalization of the discovery of the strong order chains. This generalization connects the theory of Macdonald polynomials to quantum Schubert calculus. In particular, the approach leads to conjecture that all elements in a defining set of 3-point genus 0 Gromov-Witten invariants for flag manifolds can be formulated as strong covers.
Author : Patricia Hersh
Publisher : American Mathematical Soc.
ISBN 13 : 1470427249
Total Pages : 369 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Mathematical Legacy of Richard P. Stanley written by Patricia Hersh and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.
Author : Mikhail Khovanov
Publisher : American Mathematical Soc.
ISBN 13 : 082188977X
Total Pages : 100 pages
Book Rating : 4.8/5 (218 download)
Download or read book Extended Graphical Calculus for Categorified Quantum sl(2) written by Mikhail Khovanov and published by American Mathematical Soc.. This book was released on 2012 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an earlier paper, Aaron D. Lauda constructed a categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2); here he, Khovanov, Marco Mackaay, and Marko Stosic enhance the graphical calculus he introduced to include two-morphisms between divided powers one-morphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms, which are in a bijection with the Lusztig canonical basis elements. Their results show that one of Lauda's main results holds when the 2-category is defined over the ring of integers rather than over a field. The study is not indexed. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Author :
Publisher :
ISBN 13 :
Total Pages : 448 pages
Book Rating : 4.5/5 (444 download)
Download or read book Report written by and published by . This book was released on 1996 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ezra Miller
Publisher : Springer Science & Business Media
ISBN 13 : 9780387237077
Total Pages : 442 pages
Book Rating : 4.2/5 (37 download)
Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author : Paolo Aluffi
Publisher : Cambridge University Press
ISBN 13 : 1108890547
Total Pages : 396 pages
Book Rating : 4.1/5 (88 download)
Download or read book Facets of Algebraic Geometry: Volume 2 written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2022-04-07 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.
