Symmetric Functions and Combinatorial Operators on Polynomials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetric Functions and Combinatorial Operators on Polynomials write by Alain Lascoux. This book was released on 2003. Symmetric Functions and Combinatorial Operators on Polynomials available in PDF, EPUB and Kindle. 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.
Symmetric functions and combinatorial operators on polynomials
Symmetric functions and combinatorial operators on polynomials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetric functions and combinatorial operators on polynomials write by Alain Lascoux. This book was released on 2003. Symmetric functions and combinatorial operators on polynomials available in PDF, EPUB and Kindle.
Symmetric Functions and Hall Polynomials
Symmetric Functions and Hall Polynomials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetric Functions and Hall Polynomials write by Ian Grant Macdonald. This book was released on 1998. Symmetric Functions and Hall Polynomials available in PDF, EPUB and Kindle. 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.
Symmetric Functions, Schubert Polynomials and Degeneracy Loci
Symmetric Functions, Schubert Polynomials and Degeneracy Loci - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetric Functions, Schubert Polynomials and Degeneracy Loci write by Laurent Manivel. This book was released on 2001. Symmetric Functions, Schubert Polynomials and Degeneracy Loci available in PDF, EPUB and Kindle. 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.
Symmetric Functions and Orthogonal Polynomials
Symmetric Functions and Orthogonal Polynomials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetric Functions and Orthogonal Polynomials write by Ian Grant Macdonald. This book was released on 1998. Symmetric Functions and Orthogonal Polynomials available in PDF, EPUB and Kindle. 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.
