k-Schur Functions and Affine Schubert Calculus, Thomas Lam; Luc Lapointe; Jennifer Morse; Anne Sch
Автор: Alexander Schmitt Название: Affine Flag Manifolds and Principal Bundles ISBN: 3034803095 ISBN-13(EAN): 9783034803090 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Affine flag manifolds are infinite dimensional versions of familiar objects such as Gra mann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.
Автор: Kurt Luoto; Stefan Mykytiuk; Stephanie van Willige Название: An Introduction to Quasisymmetric Schur Functions ISBN: 1461472997 ISBN-13(EAN): 9781461472995 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Поставка под заказ.
Описание: An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theory of Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them.
The second goal is to give a survey of results with respect to an exciting new basis of the Hopf algebra of quasisymmetric functions, whose combinatorics is analogous to that of the renowned Schur functions.
The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at least 2000 years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange, Jacobi, Glaisher, Ramanujan, Hardy, Mordell, Andrews, and others. Jacobi's elliptic function approach dates from his epic Fundamenta Nova of 1829. Here, the author employs his combinatorial/elliptic function methods to derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi's (1829) 4 and 8 squares identities to 4n2 or 4n(n+1) squares, respectively, without using cusp forms such as those of Glaisher or Ramanujan for 16 and 24 squares. These results depend upon new expansions for powers of various products of classical theta functions. This is the first time that infinite families of non-trivial exact explicit formulas for sums of squares have been found.
The author derives his formulas by utilizing combinatorics to combine a variety of methods and observations from the theory of Jacobi elliptic functions, continued fractions, Hankel or Turanian determinants, Lie algebras, Schur functions, and multiple basic hypergeometric series related to the classical groups. His results (in Theorem 5.19) generalize to separate infinite families each of the 21 of Jacobi's explicitly stated degree 2, 4, 6, 8 Lambert series expansions of classical theta functions in sections 40-42 of the Fundamental Nova. The author also uses a special case of his methods to give a derivation proof of the two Kac and Wakimoto (1994) conjectured identities concerning representations of a positive integer by sums of 4n2 or 4n(n+1) triangular numbers, respectively. These conjectures arose in the study of Lie algebras and have also recently been proved by Zagier using modular forms. George Andrews says in a preface of this book, This impressive work will undoubtedly spur others both in elliptic functions and in modular forms to build on these wonderful discoveries.'
Audience: This research monograph on sums of squares is distinguished by its diversity of methods and extensive bibliography. It contains both detailed proofs and numerous explicit examples of the theory. This readable work will appeal to both students and researchers in number theory, combinatorics, special functions, classical analysis, approximation theory, and mathematical physics.
Автор: W. Szmielew Название: From Affine to Euclidean Geometry ISBN: 9027712433 ISBN-13(EAN): 9789027712431 Издательство: Springer Рейтинг: Цена: 19139.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: William Fulton; Piotr Pragacz Название: Schubert Varieties and Degeneracy Loci ISBN: 3540645381 ISBN-13(EAN): 9783540645382 Издательство: Springer Рейтинг: Цена: 4890.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, taken from a summer school in Thurnau, aim to give an introduction to these topics, and to describe late-1990s progress on these problems.
Автор: Contou-Carrere Название: Buildings & Schubert Schemes ISBN: 1498768296 ISBN-13(EAN): 9781498768290 Издательство: Taylor&Francis Рейтинг: Цена: 29093.00 р. Наличие на складе: Поставка под заказ.
Описание:
The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k (r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k (r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.
Автор: Masuda Kayo Et Al Название: Affine Algebraic Geometry - Proceedings Of The Conference ISBN: 9814436690 ISBN-13(EAN): 9789814436694 Издательство: World Scientific Publishing Рейтинг: Цена: 19008.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during 3-6 March 2011 and is dedicated to Professor Masayoshi Miyanishi on the occasion of his 70th birthday. It contains 16 refereed articles in the areas of affine algebraic geometry, commutative algebra and related fields, which have been the working fields of Professor Miyanishi for almost 50 years. Readers will be able to find recent trends in these areas too. The topics contain both algebraic and analytic, as well as both affine and projective, problems. All the results treated in this volume are new and original which subsequently will provide fresh research problems to explore. This volume is suitable for graduate students and researchers in these areas.
Автор: Kazuhiko Ozeki Название: Theory of Affine Projection Algorithms for Adaptive Filtering ISBN: 4431563105 ISBN-13(EAN): 9784431563105 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book focuses on theoretical aspects of the affine projection algorithm (APA) for adaptive filtering.
Автор: Arno van den Essen Название: Automorphisms of Affine Spaces ISBN: 0792335236 ISBN-13(EAN): 9780792335238 Издательство: Springer Рейтинг: Цена: 20956.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This work describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, linearization and tame generators conjectures. Group actions and dynamical systems play a dominant role.
Автор: Ivan Cheltsov; Ciro Ciliberto; Hubert Flenner; Jam Название: Automorphisms in Birational and Affine Geometry ISBN: 3319056808 ISBN-13(EAN): 9783319056807 Издательство: Springer Рейтинг: Цена: 22359.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional.
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