# Topics In Representation Theory

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## Representation Theory of Algebras and Related Topics

Author | : Raymundo Bautista,Roberto Martínez-Villa,José Antonio de la Peña,Workshop on Representation Theory of Algebras and Related Topics (1994 : Mexico City, Mexico) |

Publsiher | : American Mathematical Soc. |

Total Pages | : 406 |

Release | : 1996 |

ISBN | : 9780821803967 |

Category | : Mathematics |

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

**Representation Theory of Algebras and Related Topics Book Excerpt:**

These proceedings report a number of lecture series delivered during the Workshop on Representation Theory of Algebras and Related Topics held at Universidad Nacional Autonoma de Mexico (UNAM) in August 1994. The workshop was dedicated to recent advances in the field and its interaction with other areas of mathematics, such as algebraic geometry, ring theory, and representation of groups. The program of the Workshop consisted of 9 lecture series. In addition there was a Tame Day consisting of 6 lectures reporting on the recent advances in the study of tame algebras and their module categories. During the Workshop there was a session devoted to the exhibition of computer programs developed by participants. These programs are implementations of algorithms related to the calculation of important aspects of algebras and their module categories.

## Trends in Representation Theory of Algebras and Related Topics

Author | : Andrzej Skowroński |

Publsiher | : European Mathematical Society |

Total Pages | : 710 |

Release | : 2008 |

ISBN | : 9783037190623 |

Category | : Mathematics |

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

**Trends in Representation Theory of Algebras and Related Topics Book Excerpt:**

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

## Trends in Representation Theory of Algebras and Related Topics

Author | : José Antonio de la Peña,Raymundo Bautista |

Publsiher | : American Mathematical Soc. |

Total Pages | : 270 |

Release | : 2006 |

ISBN | : 0821838180 |

Category | : Mathematics |

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

**Trends in Representation Theory of Algebras and Related Topics Book Excerpt:**

This book is based on lectures given during a Workshop on Representations of Algebras and Related Topics. Some additional articles are included in order to complete a panoramic view of the main trends of the subject. The volume contains original presentations by leading algebraists addressed to specialists as well as to a broader mathematical audience. The articles include new proofs, examples, and detailed arguments. Topics under discussion include moduli spaces associated to quivers, canonical basis of quantum algebras, categorifications and derived categories, $A$-infinity algebras and functor categories, cluster algebras, support varieties for modules and complexes, the Gabriel-Roiter measure for modules, and selfinjective algebras.

## Representation Theory of Finite Groups and Related Topics

Author | : Irving Reiner,American Mathematical Society |

Publsiher | : American Mathematical Soc. |

Total Pages | : 178 |

Release | : 1971 |

ISBN | : 0821814214 |

Category | : Mathematics |

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

**Representation Theory of Finite Groups and Related Topics Book Excerpt:**

## Complements of Discriminants of Smooth Maps

Author | : Zongzhu Lin,Jianpan Wang |

Publsiher | : American Mathematical Soc. |

Total Pages | : 295 |

Release | : 2009-01-16 |

ISBN | : 0821845551 |

Category | : Mathematics |

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

**Complements of Discriminants of Smooth Maps Book Excerpt:**

Nothing provided

## Introduction to Representation Theory

Author | : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina |

Publsiher | : American Mathematical Soc. |

Total Pages | : 228 |

Release | : 2011 |

ISBN | : 0821853511 |

Category | : Mathematics |

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

**Introduction to Representation Theory Book Excerpt:**

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. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

## Representation Theory of Finite Groups and Finite Dimensional Algebras

Author | : Michler,Ringel |

Publsiher | : Birkhäuser |

Total Pages | : 522 |

Release | : 2012-12-06 |

ISBN | : 3034886586 |

Category | : Mathematics |

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

**Representation Theory of Finite Groups and Finite Dimensional Algebras Book Excerpt:**

From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.

## Group Representation for Quantum Theory

Author | : Masahito Hayashi |

Publsiher | : Springer |

Total Pages | : 338 |

Release | : 2016-11-18 |

ISBN | : 3319449060 |

Category | : Science |

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

**Group Representation for Quantum Theory Book Excerpt:**

This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory. Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions.

## Topics in Representation Theory

Author | : Aleksandr Aleksandrovich Kirillov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 247 |

Release | : 1991 |

ISBN | : 9780821841013 |

Category | : Mathematics |

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

**Topics in Representation Theory Book Excerpt:**

Almost every major mathematical theory, from 19th century classical analysis and geometry to the newest abstract constructions of category theory, have recently acquired a ""physical flavour"". In the case of representation theory, two new areas of mathematical physics - the theory of completely integrable systems and string theory - have had a great influence. In addition, the idea of supersymmetry has become a general mathematical principle that has had important ramifications in representation theory. Together with this wave of new connections and new trends in representation theory, more traditional activity, dealing mostly with the study of classical objects, has also flourished. The papers in this volume were written by members of the seminar on representation theory at Moscow University, which has been running continuously since 1961. The papers reflect some of the new influences seen in representation theory today. Among the topics included are representation theory of ""large"" groups, indecomposable representations of the affine unimodular group of the plane, dual objects for certain real reductive Lie groups, and geometrical interpretations of a certain infinite-dimensional Lie algebra.

## Lectures on Representation Theory

Author | : Jing-Song Huang |

Publsiher | : World Scientific |

Total Pages | : 189 |

Release | : 1999 |

ISBN | : 9789810237257 |

Category | : Mathematics |

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

**Lectures on Representation Theory Book Excerpt:**

This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.

## Representations of Algebras and Related Topics

Author | : Ragnar-Olaf Buchweitz,Helmut Lenzing |

Publsiher | : American Mathematical Soc. |

Total Pages | : 396 |

Release | : 2022 |

ISBN | : 9780821885925 |

Category | : Mathematics |

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

**Representations of Algebras and Related Topics Book Excerpt:**

This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.

## Representation theory of finite groups and related topics

Author | : Shigeo Koshitani |

Publsiher | : Unknown |

Total Pages | : 123 |

Release | : 2000 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

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

**Representation theory of finite groups and related topics Book Excerpt:**

## Representation Theory of Finite Groups

Author | : Martin Burrow |

Publsiher | : Academic Press |

Total Pages | : 196 |

Release | : 2014-05-10 |

ISBN | : 1483258211 |

Category | : Mathematics |

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

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

Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

## Integral Representations

Author | : I. Reiner,K.W. Roggenkamp |

Publsiher | : Springer |

Total Pages | : 281 |

Release | : 2006-11-15 |

ISBN | : 3540350071 |

Category | : Mathematics |

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

**Integral Representations Book Excerpt:**

## Fundamentals of Infinite Dimensional Representation Theory

Author | : Raymond C. Fabec |

Publsiher | : CRC Press |

Total Pages | : 448 |

Release | : 2000-06-28 |

ISBN | : 9781584882121 |

Category | : Mathematics |

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

**Fundamentals of Infinite Dimensional Representation Theory Book Excerpt:**

Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

## Representation of Lie Groups and Related Topics

Author | : Anatoliĭ Moiseevich Vershik,Dmitriĭ Petrovich Zhelobenko |

Publsiher | : CRC Press |

Total Pages | : 557 |

Release | : 1990 |

ISBN | : 9782881246784 |

Category | : Mathematics |

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

**Representation of Lie Groups and Related Topics Book Excerpt:**

Eight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

## Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

Author | : Vlastimil Dlab,Claus Michael Ringel |

Publsiher | : American Mathematical Soc. |

Total Pages | : 479 |

Release | : 2022 |

ISBN | : 9780821871454 |

Category | : Mathematics |

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

**Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry Book Excerpt:**

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.

## Representation Theory

Author | : William Fulton,Joe Harris |

Publsiher | : Springer Science & Business Media |

Total Pages | : 551 |

Release | : 2013-12-01 |

ISBN | : 146120979X |

Category | : Mathematics |

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

**Representation Theory Book Excerpt:**

The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.

## Group Representation Theory

Author | : Meinolf Geck |

Publsiher | : EPFL Press |

Total Pages | : 454 |

Release | : 2007-05-07 |

ISBN | : 9780849392436 |

Category | : Mathematics |

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

**Group Representation Theory Book Excerpt:**

After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).

## Representation Theory of Finite Groups and Associative Algebras

Author | : Charles W. Curtis,Irving Reiner |

Publsiher | : American Mathematical Soc. |

Total Pages | : 689 |

Release | : 1966 |

ISBN | : 9780821869451 |

Category | : Mathematics |

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

**Representation Theory of Finite Groups and Associative Algebras Book Excerpt:**