Schur Algebras And Representation Theory

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Schur Algebras and Representation Theory

Stuart Martin
Schur Algebras and Representation Theory Book PDF

Author : Stuart Martin
Publisher : Cambridge University Press
Page : 256 pages
File Size : 42,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780521415910

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Schur Algebras and Representation Theory by Stuart Martin Pdf

The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it will be of interest to all research workers in representation theory.

The Q-Schur Algebra

Stephen Donkin
The Q Schur Algebra Book PDF

Author : Stephen Donkin
Publisher : Cambridge University Press
Page : 193 pages
File Size : 51,8 Mb
Release : 1998-12-10
Category : Mathematics
ISBN : 9780521645584

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The Q-Schur Algebra by Stephen Donkin Pdf

This book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. The aim is to present, from a unified point of view, quantum analogs of certain results known already in the classical case. The approach is largely homological, based on Kempf's vanishing theorem for quantum groups and the quasi-hereditary structure of the q-Schur algebras. Beginning with an introductory chapter dealing with the relationship between the ordinary general linear groups and their quantum analogies, the text goes on to discuss the Schur Functor and the 0-Schur algebra. The next chapter considers Steinberg's tensor product and infinitesimal theory. Later sections of the book discuss tilting modules, the Ringel dual of the q-Schur algebra, Specht modules for Hecke algebras, and the global dimension of the q-Schur algebras. An appendix gives a self-contained account of the theory of quasi-hereditary algebras and their associated tilting modules. This volume will be primarily of interest to researchers in algebra and related topics in pure mathematics.

Representation Theory

Amritanshu Prasad
Representation Theory Book PDF

Author : Amritanshu Prasad
Publisher : Cambridge University Press
Page : 205 pages
File Size : 44,9 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9781107082052

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Representation Theory by Amritanshu Prasad Pdf

This book examines the fundamental results of modern combinatorial representation theory. The exercises are interspersed with text to reinforce readers' understanding 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.

Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group

Andrew Mathas
Iwahori Hecke Algebras and Schur Algebras of the Symmetric Group Book PDF

Author : Andrew Mathas
Publisher : American Mathematical Soc.
Page : 204 pages
File Size : 52,8 Mb
Release : 1999
Category : Representations of algebras
ISBN : 9780821819265

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Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group by Andrew Mathas Pdf

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. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and $q$-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the $q$-Schur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers.

Algebras and Representation Theory

Karin Erdmann,Thorsten Holm
Algebras and Representation Theory Book PDF

Author : Karin Erdmann,Thorsten Holm
Publisher : Springer
Page : 304 pages
File Size : 52,9 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783319919980

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Algebras and Representation Theory by Karin Erdmann,Thorsten Holm Pdf

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.

Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer

Charles W. Curtis
Pioneers of Representation Theory Frobenius Burnside Schur and Brauer Book PDF

Author : Charles W. Curtis
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 49,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821826775

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Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer by Charles W. Curtis Pdf

The AMS History of Mathematics series is one of the most popular items for bookstore sales. These books feature colorful, attractive covers that are perfect for face out displays. The topics will appeal to a broad audience in the mathematical and scientific communities.

The Q-Schur Algebra

S. Donkin
The Q Schur Algebra Book PDF

Author : S. Donkin
Publisher : Unknown
Page : 192 pages
File Size : 41,7 Mb
Release : 1999
Category : Electronic books
ISBN : 1107367646

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The Q-Schur Algebra by S. Donkin Pdf

This book focuses on the representation theory of q-Schur algebras.

Introduction to Representation Theory

Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Introduction to Representation Theory Book PDF

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 43,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

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Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

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.

A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory

Bangming Deng,Jie Du,Qiang Fu
A Double Hall Algebra Approach to Affine Quantum Schur Weyl Theory Book PDF

Author : Bangming Deng,Jie Du,Qiang Fu
Publisher : Cambridge University Press
Page : 217 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781107608603

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A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory by Bangming Deng,Jie Du,Qiang Fu Pdf

The first book of its kind to present an algebraic approach to affine q-Schur algebras and affine quantum Schur-Weyl theory.

Polynomial Representations of GL_n

James A. Green
Polynomial Representations of GL n Book PDF

Author : James A. Green
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 46,9 Mb
Release : 2006-11-30
Category : Mathematics
ISBN : 9783540469445

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Polynomial Representations of GL_n by James A. Green Pdf

The new corrected and expanded edition adds a special appendix on Schensted Correspondence and Littelmann Paths. This appendix can be read independently of the rest of the volume and is an account of the Littelmann path model for the case gln. The appendix also offers complete proofs of classical theorems of Schensted and Knuth.

Polynomial Representations of GL_n

James A. Green
Polynomial Representations of GL n Book PDF

Author : James A. Green
Publisher : Springer
Page : 124 pages
File Size : 44,9 Mb
Release : 2008-07-15
Category : Mathematics
ISBN : 9783540383796

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Polynomial Representations of GL_n by James A. Green Pdf

The new corrected and expanded edition adds a special appendix on Schensted Correspondence and Littelmann Paths. This appendix can be read independently of the rest of the volume and is an account of the Littelmann path model for the case gln. The appendix also offers complete proofs of classical theorems of Schensted and Knuth.

Homological Theory of Representations

Henning Krause
Homological Theory of Representations Book PDF

Author : Henning Krause
Publisher : Cambridge University Press
Page : 517 pages
File Size : 51,7 Mb
Release : 2021-11-18
Category : Mathematics
ISBN : 9781108838894

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Homological Theory of Representations by Henning Krause Pdf

This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Alexey P Isaev,Valery A Rubakov
Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications Book PDF

Author : Alexey P Isaev,Valery A Rubakov
Publisher : World Scientific
Page : 615 pages
File Size : 50,7 Mb
Release : 2020-07-16
Category : Science
ISBN : 9789811217425

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Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by Alexey P Isaev,Valery A Rubakov Pdf

This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

Representation Theory of Symmetric Groups

Pierre-Loic Meliot
Representation Theory of Symmetric Groups Book PDF

Author : Pierre-Loic Meliot
Publisher : CRC Press
Page : 433 pages
File Size : 49,5 Mb
Release : 2017-05-12
Category : Mathematics
ISBN : 9781315353852

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Representation Theory of Symmetric Groups by Pierre-Loic Meliot Pdf

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.

A Journey Through Representation Theory

Caroline Gruson,Vera Serganova
A Journey Through Representation Theory Book PDF

Author : Caroline Gruson,Vera Serganova
Publisher : Springer
Page : 223 pages
File Size : 49,9 Mb
Release : 2018-10-23
Category : Mathematics
ISBN : 9783319982717

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A Journey Through Representation Theory by Caroline Gruson,Vera Serganova Pdf

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.