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Author :
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (923 download)
Download or read book Universal Schubert Polynomials written by and published by . This book was released on 1997 with total page 20 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 : 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 : 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 : Avery J St. Dizier
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (124 download)
Download or read book Combinatorics of Schubert Polynomials written by Avery J St. Dizier and published by . This book was released on 2020 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study several aspects of the combinatorics of various important families of polynomials, particularly focusing on Schubert polynomials. Schubert polynomials arise as distinguished representatives of cohomology classes in the cohomology ring of the flag variety. As polynomials, they enjoy a rich and well-studied combinatorics. Through joint works with Fink and M\'esz\'aros, we connect the supports of Schubert polynomials to a class of polytopes called generalized permutahedra. Through a realization of Schubert polynomials as characters of flagged Weyl modules, we show that the exponents of a Schubert polynomial are exactly the integer points in a generalized permutahedron. We also prove a combinatorial description of this permutahedron. We then study characters of flagged Weyl modules more generally and give an interesting inequality on their coefficients. We next shift our focus onto the coefficients of Schubert polynomials. We describe a construction due to Magyar called orthodontia. We use orthodontia together with the previous inequality for characters to give a complete description of the Schubert polynomials that have only zero and one as coefficients. Through joint work with Huh, Matherne, and M\'esz\'aros, we next show a discrete log-concavity property of the coefficients of Schubert polynomials. The main tool for this purpose is the Lorentzian property introduced by Br\"and\'en and Huh. We prove that something similar to Schubert polynomials is Lorentzian. We extract from this the discrete log-concavity of Schubert polynomials and the Lorentzian property of Schur polynomials. We finish with various conjectures and partial results regarding other families of polynomials.
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 : Sergej Vasilʹevič Fomin
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (186 download)
Download or read book Schubert Polynomials and the NilCoxeter Algebra written by Sergej Vasilʹevič Fomin and published by . This book was released on 1992 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nantel Bergeron
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.:/5 (258 download)
Download or read book Schubert Polynomials, the Bruhat Order, and the Geometry of Flag Manifolds written by Nantel Bergeron and published by . This book was released on 1996 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudolf Winkel
Publisher :
ISBN 13 :
Total Pages : 223 pages
Book Rating : 4.:/5 (637 download)
Download or read book On Algebraic and Combinatorial Properties of Schur and Schubert Polynomials written by Rudolf Winkel and published by . This book was released on 2000 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : Sara Amato
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (112 download)
Download or read book Schubert Polynomial Multiplication written by Sara Amato and published by . This book was released on 2019 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Anderson
Publisher : Cambridge University Press
ISBN 13 : 1009349961
Total Pages : 464 pages
Book Rating : 4.0/5 (93 download)
Download or read book Equivariant Cohomology in Algebraic Geometry written by David Anderson and published by Cambridge University Press. This book was released on 2023-10-26 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.
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 : Graham J. Leuschke
Publisher : American Mathematical Soc.
ISBN 13 : 1470435764
Total Pages : 294 pages
Book Rating : 4.4/5 (74 download)
Download or read book Representations of Algebras written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2018 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held in August 2016, at Syracuse University. This volume includes three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories.
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.
