# Representation Theory

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## Representation Theory

Author | : Amritanshu Prasad |

Publsiher | : Cambridge University Press |

Total Pages | : 191 |

Release | : 2015-02-05 |

ISBN | : 1316222705 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representation Theory Book Excerpt:**

This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background. An important highlight of this book is an innovative treatment of the Robinson–Schensted–Knuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of Schur–Weyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.

## Principal Structures and Methods of Representation Theory

Author | : Dmitriĭ Petrovich Zhelobenko |

Publsiher | : American Mathematical Soc. |

Total Pages | : 430 |

Release | : 2022 |

ISBN | : 9780821889671 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Principal Structures and Methods of Representation Theory Book Excerpt:**

The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups,along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Liealgebras and Lie groups, Banach algebras, and quantum groups. This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading. Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.

## Representation Theory

Author | : Edwin Williams |

Publsiher | : MIT Press |

Total Pages | : 295 |

Release | : 2002-12-20 |

ISBN | : 9780262265072 |

Category | : Language Arts & Disciplines |

Language | : EN, FR, DE, ES & NL |

**Representation Theory Book Excerpt:**

In this theoretical monograph, Edwin Williams demonstrates that when syntax is economical, it economizes on shape distortion rather than on distance. According to Williams, this new notion of economy calls for a new architecture for the grammatical system—in fact, for a new notion of derivation. The new architecture offers a style of clausal embedding—the Level Embedding Scheme—that predictively ties together the locality, reconstructive behavior, and "target" type of any syntactic process in a way that is unique to the model. Williams calls his theory "Representation Theory" to put the notion of economy at the forefront. Syntax, in this theory, is a series of representations of one sublanguage in another.

## Vector Bundles and Representation Theory

Author | : Vector Bundles Conference on Hilbert Schemes |

Publsiher | : American Mathematical Soc. |

Total Pages | : 244 |

Release | : 2003 |

ISBN | : 0821832646 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Vector Bundles and Representation Theory Book Excerpt:**

This volume contains 13 papers from the conference on 'Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory'. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S^1$ fixed points in Quot-schemes and mirror principle computations for Grassmannians by S.T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

## Algebra Representation Theory

Author | : Klaus W. Roggenkamp,Mirela Stefanescu |

Publsiher | : Springer Science & Business Media |

Total Pages | : 460 |

Release | : 2001-08-31 |

ISBN | : 9780792371137 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Algebra Representation Theory Book Excerpt:**

Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.

## Representation Theory and Beyond

Author | : Jan Šťovíček,Jan Trlifaj |

Publsiher | : American Mathematical Soc. |

Total Pages | : 298 |

Release | : 2020-11-13 |

ISBN | : 147045131X |

Category | : Education |

Language | : EN, FR, DE, ES & NL |

**Representation Theory and Beyond Book Excerpt:**

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

## Basic Representation Theory of Algebras

Author | : Ibrahim Assem,Flávio U. Coelho |

Publsiher | : Springer Nature |

Total Pages | : 311 |

Release | : 2020-04-03 |

ISBN | : 3030351181 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Basic Representation Theory of Algebras Book Excerpt:**

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.

## Representation Theory of Symmetric Groups

Author | : Pierre-Loic Meliot |

Publsiher | : CRC Press |

Total Pages | : 666 |

Release | : 2017-05-12 |

ISBN | : 1315353857 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representation Theory of Symmetric Groups Book Excerpt:**

Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.

## Algebras and Representation Theory

Author | : Karin Erdmann,Thorsten Holm |

Publsiher | : Springer |

Total Pages | : 298 |

Release | : 2018-09-07 |

ISBN | : 3319919989 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Algebras and Representation Theory Book Excerpt:**

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

## A Tour of Representation Theory

Author | : Martin Lorenz |

Publsiher | : American Mathematical Soc. |

Total Pages | : 654 |

Release | : 2018 |

ISBN | : 1470436809 |

Category | : Categories (Mathematics) |

Language | : EN, FR, DE, ES & NL |

**A Tour of Representation Theory Book Excerpt:**

Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.

## Operators and Representation Theory

Author | : Palle E.T. Jorgensen |

Publsiher | : Courier Dover Publications |

Total Pages | : 304 |

Release | : 2017-05-22 |

ISBN | : 0486822575 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Operators and Representation Theory Book Excerpt:**

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

## Surveys in Representation Theory of Algebras

Author | : Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 203 |

Release | : 2018-09-12 |

ISBN | : 1470436795 |

Category | : Representations of algebras |

Language | : EN, FR, DE, ES & NL |

**Surveys in Representation Theory of Algebras Book Excerpt:**

This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.

## The Representation Theory of Finite Groups

Author | : W. Feit |

Publsiher | : Elsevier |

Total Pages | : 501 |

Release | : 1982-05-01 |

ISBN | : 9780080960135 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**The Representation Theory of Finite Groups Book Excerpt:**

The Representation Theory of Finite Groups

## Integral Geometry and Representation Theory

Author | : I. M. Gel'fand,M. I. Graev,N. Ya. Vilenkin |

Publsiher | : Academic Press |

Total Pages | : 468 |

Release | : 2014-05-12 |

ISBN | : 1483262251 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Integral Geometry and Representation Theory Book Excerpt:**

Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

## Representation Theory of Finite Groups

Author | : Martin Burrow |

Publsiher | : Courier Corporation |

Total Pages | : 185 |

Release | : 1965 |

ISBN | : 0486674878 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representation Theory of Finite Groups Book Excerpt:**

Concise, graduate-level exposition of the theory of finite groups, including the theory of modular representations. Topics include representation theory of rings with identity, representation theory of finite groups, applications of the theory of characters, construction of irreducible representations and modular representations. Rudiments of linear algebra and knowledge of group theory helpful prerequisites. Exercises. Bibliography. Appendix. 1965 edition.

## Representation Theory of Finite Monoids

Author | : Benjamin Steinberg |

Publsiher | : Springer |

Total Pages | : 320 |

Release | : 2016-12-09 |

ISBN | : 3319439324 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representation Theory of Finite Monoids Book Excerpt:**

This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.

## Symmetry Representation Theory and Its Applications

Author | : Roger Howe,Markus Hunziker,Jeb F. Willenbring |

Publsiher | : Springer |

Total Pages | : 538 |

Release | : 2015-01-04 |

ISBN | : 1493915908 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Symmetry Representation Theory and Its Applications Book Excerpt:**

Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.

## Geometry of Moduli Spaces and Representation Theory

Author | : Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun |

Publsiher | : American Mathematical Soc. |

Total Pages | : 436 |

Release | : 2017-12-15 |

ISBN | : 1470435748 |

Category | : Algebraic varieties |

Language | : EN, FR, DE, ES & NL |

**Geometry of Moduli Spaces and Representation Theory Book Excerpt:**

This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.

## Representation Theory Group Rings and Coding Theory

Author | : M. Isaacs |

Publsiher | : American Mathematical Soc. |

Total Pages | : 357 |

Release | : 1989 |

ISBN | : 0821850989 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representation Theory Group Rings and Coding Theory Book Excerpt:**

This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.

## Elements of the Representation Theory of the Jacobi Group

Author | : Rolf Berndt,Ralf Schmidt |

Publsiher | : Springer Science & Business Media |

Total Pages | : 213 |

Release | : 2012-01-03 |

ISBN | : 3034802838 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Elements of the Representation Theory of the Jacobi Group Book Excerpt:**

Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.