Representation Theory And Algebraic Geometry

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Representation Theory and Algebraic Geometry

Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Representation Theory and Algebraic Geometry Book PDF

Author : Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Publisher : Birkhäuser
Page : 0 pages
File Size : 51,8 Mb
Release : 2023-06-17
Category : Mathematics
ISBN : 3030820092

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Representation Theory and Algebraic Geometry by Vladimir Baranovsky,Nicolas Guay,Travis Schedler Pdf

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Representation Theories and Algebraic Geometry

A. Broer
Representation Theories and Algebraic Geometry Book PDF

Author : A. Broer
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 54,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401591317

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Representation Theories and Algebraic Geometry by A. Broer Pdf

The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Representation Theory and Algebraic Geometry

A. Martsinkovsky,Gordana Todorov
Representation Theory and Algebraic Geometry Book PDF

Author : A. Martsinkovsky,Gordana Todorov
Publisher : Cambridge University Press
Page : 148 pages
File Size : 43,6 Mb
Release : 1997-05-15
Category : Mathematics
ISBN : 0521577896

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Representation Theory and Algebraic Geometry by A. Martsinkovsky,Gordana Todorov Pdf

For any researcher working in representation theory, algebraic or arithmetic geometry.

Noncommutative Algebraic Geometry and Representations of Quantized Algebras

A. Rosenberg
Noncommutative Algebraic Geometry and Representations of Quantized Algebras Book PDF

Author : A. Rosenberg
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 55,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584302

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Noncommutative Algebraic Geometry and Representations of Quantized Algebras by A. Rosenberg Pdf

This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.

Representation Theory and Complex Geometry

Neil Chriss
Representation Theory and Complex Geometry Book PDF

Author : Neil Chriss
Publisher : Birkhauser
Page : 495 pages
File Size : 53,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9780817637927

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Representation Theory and Complex Geometry by Neil Chriss Pdf

This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.

Representation Theory of Algebraic Groups and Quantum Groups

Toshiaki Shoji
Representation Theory of Algebraic Groups and Quantum Groups Book PDF

Author : Toshiaki Shoji
Publisher : American Mathematical Society(RI)
Page : 514 pages
File Size : 43,6 Mb
Release : 2004
Category : Computers
ISBN : UOM:39015061859339

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Representation Theory of Algebraic Groups and Quantum Groups by Toshiaki Shoji Pdf

A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.

Algebraic Combinatorics and Coinvariant Spaces

Francois Bergeron
Algebraic Combinatorics and Coinvariant Spaces Book PDF

Author : Francois Bergeron
Publisher : CRC Press
Page : 227 pages
File Size : 54,5 Mb
Release : 2009-07-06
Category : Mathematics
ISBN : 9781439865071

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Algebraic Combinatorics and Coinvariant Spaces by Francois Bergeron Pdf

Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and

Frobenius Splitting Methods in Geometry and Representation Theory

Michel Brion,Shrawan Kumar
Frobenius Splitting Methods in Geometry and Representation Theory Book PDF

Author : Michel Brion,Shrawan Kumar
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 40,8 Mb
Release : 2007-08-08
Category : Mathematics
ISBN : 9780817644055

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Frobenius Splitting Methods in Geometry and Representation Theory by Michel Brion,Shrawan Kumar Pdf

Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.

D-Modules, Perverse Sheaves, and Representation Theory

Ryoshi Hotta,Toshiyuki Tanisaki
D Modules Perverse Sheaves and Representation Theory Book PDF

Author : Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 55,9 Mb
Release : 2007-11-07
Category : Mathematics
ISBN : 9780817643638

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D-Modules, Perverse Sheaves, and Representation Theory by Ryoshi Hotta,Toshiyuki Tanisaki Pdf

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.

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 : 52,6 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.

Algebra - Representation Theory

Klaus W. Roggenkamp,Mirela Stefanescu
Algebra Representation Theory Book PDF

Author : Klaus W. Roggenkamp,Mirela Stefanescu
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 43,5 Mb
Release : 2001-08-31
Category : Mathematics
ISBN : 0792371135

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Algebra - Representation Theory by Klaus W. Roggenkamp,Mirela Stefanescu Pdf

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.

Geometry of Moduli Spaces and Representation Theory

Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Geometry of Moduli Spaces and Representation Theory Book PDF

Author : Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 52,6 Mb
Release : 2017-12-15
Category : Algebraic varieties
ISBN : 9781470435745

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Geometry of Moduli Spaces and Representation Theory by Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun Pdf

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 of Finite Groups: Algebra and Arithmetic

Steven H. Weintraub
Representation Theory of Finite Groups Algebra and Arithmetic Book PDF

Author : Steven H. Weintraub
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 40,7 Mb
Release : 2003
Category : Finite groups
ISBN : 9780821832226

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Representation Theory of Finite Groups: Algebra and Arithmetic by Steven H. Weintraub Pdf

``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.

Representation Theory and Algebraic Geometry

Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Representation Theory and Algebraic Geometry Book PDF

Author : Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Publisher : Springer Nature
Page : 458 pages
File Size : 45,8 Mb
Release : 2022-06-15
Category : Mathematics
ISBN : 9783030820077

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Representation Theory and Algebraic Geometry by Vladimir Baranovsky,Nicolas Guay,Travis Schedler Pdf

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Introduction to Lie Algebras and Representation Theory

J.E. Humphreys
Introduction to Lie Algebras and Representation Theory Book PDF

Author : J.E. Humphreys
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263982

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Introduction to Lie Algebras and Representation Theory by J.E. Humphreys Pdf

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.