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The modular representation theory of Iwahori-Hecke algebras and this theory's 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 Ariki's 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.

Hardcover:

9780857297150 | Springer Verlag, June 1, 2011, cover price $139.00 | About this edition: The modular representation theory of Iwahori-Hecke algebras and this theory's 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.

Paperback:

9781447126577 | Springer Verlag, July 15, 2013, cover price $139.00

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Product Description: * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics...read more

Hardcover:

9780817634087 | Birkhauser, December 1, 2003, cover price $124.00 | About this edition: * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples.

Paperback:

9781461264804 | Reprint edition (Birkhauser, October 2, 2012), cover price $124.00 | About this edition: * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples.

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Product Description: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory...read more

Paperback:

9780821853511 | Amer Mathematical Society, August 11, 2011, cover price $45.00 | About this edition: Very roughly speaking, representation theory studies symmetry in linear spaces.

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Product Description: The emergence of The United Nations Peacebuilding Commission (PBC) in 2005 was the culmination of a long and contentious process. In this work Rob Jenkins provides a concise introduction that traces the origins and evolution of peacebuilding as a concept, the creation and functioning of the PBC as an institution, and the complicated relationship between these two processes...read more

Hardcover:

9781107005969 | Cambridge Univ Pr, August 15, 2011, cover price $95.99 | About this edition: The emergence of The United Nations Peacebuilding Commission (PBC) in 2005 was the culmination of a long and contentious process.

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Product Description: This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras...read more

Paperback:

9780521757683 | 1 edition (Cambridge Univ Pr, October 30, 2009), cover price $119.00 | About this edition: This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules.

By Pramod Kanwar (editor)

Paperback:

9780821843703, titled "Rings, Modules and Representations: International Conference on Rings and Things in Honor of Carl Faith and Barbara Osofsky June 15-17, 2007, Ohio Univeristy-zanesville, Zanesville, Oh" | Amer Mathematical Society, February 27, 2009, cover price $104.00

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Product Description: Schur algebras are an algebraic system that provide a link between the representation theory of the symmetric and general linear groups. Dr. Martin gives a self-contained account of this algebra and those links, covering the basic ideas and their quantum analogues...read more

Hardcover:

9780521415910 | Cambridge Univ Pr, December 1, 1993, cover price $164.99 | About this edition: Schur algebras are an algebraic system that provide a link between the representation theory of the symmetric and general linear groups.

Paperback:

9780521100465 | 1 edition (Cambridge Univ Pr, January 18, 2009), cover price $64.99 | About this edition: Schur algebras are an algebraic system that provide a link between the representation theory of the symmetric and general linear groups.

cover image for 9780486466651
Product Description: Algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional. This book begins with extensive background material that covers definitions and terminology, operators in Hilbert space, and the imprimitivity theorem...read more

Paperback:

9780486466651 | Dover Pubns, May 19, 2008, cover price $19.95 | About this edition: Algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional.
9780444703217 | Elsevier Science Ltd, December 1, 1987, cover price $144.50 | About this edition: Historically, operator theory and representation theory both originated with the advent of quantum mechanics.

cover image for 9783037190340
Product Description: Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc...read more

Paperback:

9783037190340 | Amer Mathematical Society, March 15, 2007, cover price $34.00 | About this edition: Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians.

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Product Description: Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis...read more

Paperback:

9780387260402 | Springer Verlag, October 30, 2006, cover price $64.95 | About this edition: Lie groups has been an increasing area of focus and rich research since the middle of the 20th century.

cover image for 9780821839164
Product Description: Various subsets of the tracial state space of a unital $C^*$-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II$_1$-factor representations of a class of $C^*$-algebras considered by Sorin Popa are also studied...read more

Paperback:

9780821839164 | Amer Mathematical Society, October 6, 2006, cover price $65.00 | About this edition: Various subsets of the tracial state space of a unital $C^*$-algebra are studied.

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Product Description: Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N...read more

Hardcover:

9780805316001 | Benjamin-Cummings Pub Co, June 1, 1984, cover price $33.75 | About this edition: Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories.

Paperback:

9780486449999 | Dover Pubns, March 17, 2006, cover price $12.95 | About this edition: Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories.

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Product Description: This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra...read more

Hardcover:

9780521584234 | Cambridge Univ Pr, February 28, 2006, cover price $145.00 | About this edition: This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field.

Paperback:

9780521586313 | Cambridge Univ Pr, February 28, 2006, cover price $59.99 | About this edition: This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field.

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Product Description: Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of  Lie type...read more

Paperback:

9783540002246 | Springer Verlag, February 1, 2003, cover price $49.95 | About this edition: Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context.
9780070630840, titled "Aim/Far 1995: Airman''s Information Manual/Federal Aviation Regulations" | Tab Books, December 1, 1994, cover price $12.95

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Product Description: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows...read more (view table of contents, read Amazon.com's description)

Paperback:

9783540660064 | Springer Verlag, June 1, 1999, cover price $65.00 | About this edition: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality.

cover image for 9780821819265
Product Description: This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers...read more

Paperback:

9780821819265 | Amer Mathematical Society, June 1, 1999, cover price $30.00 | About this edition: This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras.

Paperback:

9780521645584 | Cambridge Univ Pr, December 1, 1998, cover price $79.99

cover image for 9780821808665
Product Description: Inspired by mathematical structures found by theoretical physicists and by the desire to understand the 'monstrous moonshine' of the Monster group, Borcherds, Frenkel, Lepowsky, and Meurman introduced the definition of vertex operator algebra (VOA)...read more (view table of contents, read Amazon.com's description)

Paperback:

9780821808665 | Amer Mathematical Society, September 1, 1998, cover price $49.00 | About this edition: Inspired by mathematical structures found by theoretical physicists and by the desire to understand the 'monstrous moonshine' of the Monster group, Borcherds, Frenkel, Lepowsky, and Meurman introduced the definition of vertex operator algebra (VOA).

cover image for 9780521636537
Product Description: This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr...read more (view table of contents, read Amazon.com's description)

Hardcover:

9780521361347 | Cambridge Univ Pr, April 26, 1991, cover price $179.99 | About this edition: This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules.

Paperback:

9780521636537 | Reprint edition (Cambridge Univ Pr, August 1, 1998), cover price $69.99 | About this edition: This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules.

cover image for 9780521636520
Product Description: The heart of the book is a lengthy introduction to the representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in some detail. (view table of contents, read Amazon.com's description)

Hardcover:

9780521361354 | Cambridge Univ Pr, May 1, 1992, cover price $78.99

Paperback:

9780521636520 | Reprint edition (Cambridge Univ Pr, August 1, 1998), cover price $74.99 | About this edition: The heart of the book is a lengthy introduction to the representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in some detail.

cover image for 9783540629900
Product Description: From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere...read more (view table of contents, read Amazon.com's description)

Paperback:

9783540629900 | Springer Verlag, November 1, 1997, cover price $139.00 | About this edition: From the reviews: ".

Paperback:

9780889117563 | Queens Univ Campus, September 1, 1997, cover price $29.95

cover image for 9780521599238
Product Description: This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra. Written by three distinguished mathematicians, it illustrates how the theory of almost split sequences is utilized within representation theory...read more (view table of contents, read Amazon.com's description)

Hardcover:

9780521411349 | Cambridge Univ Pr, January 1, 1995, cover price $157.99 | About this edition: This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra.

Paperback:

9780521599238 | Cambridge Univ Pr, June 1, 1997, cover price $109.99 | About this edition: This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra.

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