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Representations of Hecke Algebras at Roots of Unity, Geck



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Цена: 11494р.
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Автор: Geck
Название:  Representations of Hecke Algebras at Roots of Unity
Издательство: Springer
Классификация:
ISBN: 0857297155
ISBN-13(EAN): 9780857297150
Обложка/Формат: Hardback
Страницы: 413
Вес: 0.759 кг.
Дата издания: 01.05.2011
Серия: Algebra and Applications
Язык: English
Иллюстрации: 6 black & white illustrations
Размер: 234 x 156 x 24
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The modular representation theory of Iwahori-Hecke algebras and this theorys connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James (1970) characteristic-free approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Arikis theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.



Algebras, rings and their representations - proceedings of the international conference on algebras, modules and rings

Название: Algebras, rings and their representations - proceedings of the international conference on algebras, modules and rings
ISBN: 9812565981 ISBN-13(EAN): 9789812565983
Издательство: World Scientific Publishing
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Цена: 17141 р.
Наличие на складе: Поставка под заказ.

Описание: Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories. The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith.

Integral Closure / Rees Algebras, Multiplicities, Algorithms

Автор: Vasconcelos Wolmer
Название: Integral Closure / Rees Algebras, Multiplicities, Algorithms
ISBN: 3540255400 ISBN-13(EAN): 9783540255406
Издательство: Springer
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Цена: 16196 р.
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Описание: Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

Standard Integral Table Algebras Generated by a Non-real Element of Small Degree

Автор: Arad Zvi, Muzychuk Mikhail
Название: Standard Integral Table Algebras Generated by a Non-real Element of Small Degree
ISBN: 3540428518 ISBN-13(EAN): 9783540428510
Издательство: Springer
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Цена: 3652 р.
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Описание: This book is addressed to the researchers working in the theory of table algebras and association schemes. This area of algebraic combinatorics has been rapidly developed during the last decade. The volume contains further developments in the theory of table algebras. It collects several papers which deal with a classification problem for standard integral table algebras (SITA). More precisely, we consider SITA with a faithful non-real element of small degree. It turns out that such SITA with some extra conditions may be classified. This leads to new infinite series of SITA which has interesting properties. The last section of the book uses a part of obtained results in the classification of association schemes. This volume summarizes the research which was done at Bar-Ilan University in the academic year 1998/99.

Theory of Operator Algebras I

Автор: Takesaki M.
Название: Theory of Operator Algebras I
ISBN: 354042248X ISBN-13(EAN): 9783540422488
Издательство: Springer
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Цена: 15674 р.
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Описание: Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.The book's unifying theme is the Banach space duality for operator algebras. This allows the reader to recognize the affinity between operator algebras and measure theory on locally compact spaces. Very technical sections are clearly labeled and there are extensive comments by the author, a good historical background and excercises.This book is part of the subseries of the EMS on Operator Algebras and Non-Commutative Geometry.

Double Affine Hecke Algebras

Автор: Ivan Cherednik
Название: Double Affine Hecke Algebras
ISBN: 0521609186 ISBN-13(EAN): 9780521609180
Издательство: Cambridge Academ
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Цена: 8742 р.
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Описание: This is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik’s algebra, and its impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, for those who want to master the new double Hecke algebra technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter 0 and selected topics from other chapters.

Affine Hecke Algebras and Orthogonal Polynomials

Автор: I. G. Macdonald
Название: Affine Hecke Algebras and Orthogonal Polynomials
ISBN: 0521824729 ISBN-13(EAN): 9780521824729
Издательство: Cambridge Academ
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Цена: 10582 р.
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Описание: In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the Askey-Wilson polynomials, which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This first comprehensive and organised account of the subject aims to provide a unified foundation for this theory, to which the author has been a principal contributor.

It is an essentially self-contained treatment, accessible to graduate students familiar with root systems and Weyl groups. The first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.

Representations of Finite-Dimensional Algebras

Автор: Gabriel
Название: Representations of Finite-Dimensional Algebras
ISBN: 3540629904 ISBN-13(EAN): 9783540629900
Издательство: Springer
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Цена: 12016 р.
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Описание: Attempts to take us up to the point where we can find our way in the original literature. This book presents some basic material and some insights of the theory. It includes proofs for statements which in the authors` opinions are elementary, those which help further understanding.

Lie Groups, Lie Algebras, and Representations

Автор: Hall
Название: Lie Groups, Lie Algebras, and Representations
ISBN: 0387401229 ISBN-13(EAN): 9780387401225
Издательство: Springer
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Цена: 4906 р.
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Описание: This book addresses Lie groups, Lie algebras, and representation theory. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.

Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

Автор: Sabinin Lev V.
Название: Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces
ISBN: 1402025440 ISBN-13(EAN): 9781402025440
Издательство: Springer
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Цена: 11494 р.
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Описание: Describes an original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. This book should is useful for researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications, as well as for other postgraduate and advanced graduate students in mathematics.

Algebraic Integrability, PainlevГ© Geometry and Lie Algebras

Автор: Adler Mark, Moerbeke Pierre van, Vanhaecke Pol
Название: Algebraic Integrability, PainlevГ© Geometry and Lie Algebras
ISBN: 354022470X ISBN-13(EAN): 9783540224709
Издательство: Springer
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Цена: 14629 р.
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Описание: This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and PainlevГ© analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.

Symmetries, Lie Algebras and Representations

Автор: Fuchs/Schweigert
Название: Symmetries, Lie Algebras and Representations
ISBN: 0521541190 ISBN-13(EAN): 9780521541190
Издательство: Cambridge Academ
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Цена: 7821 р.
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Описание: This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers.

Representations of Lie Algebras

Автор: Henderson
Название: Representations of Lie Algebras
ISBN: 1107653614 ISBN-13(EAN): 9781107653610
Издательство: Cambridge Academ
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Цена: 4945 р.
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Описание: This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics.


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