Lectures On Representation Theory

Author : Jing-Song Huang
Publisher : World Scientific
Page : 206 pages
File Size : 51,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9810237251

Get Book

Lectures on Representation Theory by Jing-Song Huang Pdf

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.

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 : 44,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

Get Book

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.

Author : Pavel I. Etingof,Igor Frenkel,Alexander A. Kirillov
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 47,8 Mb
Release : 1998
Category : Broken symmetry (Physics).
ISBN : 9780821804964

Get Book

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations by Pavel I. Etingof,Igor Frenkel,Alexander A. Kirillov Pdf

This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

Author : Michael Cowling
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 41,9 Mb
Release : 2008-02-27
Category : Mathematics
ISBN : 9783540768913

Get Book

Representation Theory and Complex Analysis by Michael Cowling Pdf

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.

Author : William Fulton,Joe Harris
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 54,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0387974954

Get Book

Representation Theory by William Fulton,Joe Harris Pdf

Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

Author : Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 54,8 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9780821891407

Get Book

Expository Lectures on Representation Theory by Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov Pdf

This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams.

Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 49,9 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489

Get Book

Lectures on Invariant Theory by Igor Dolgachev Pdf

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Author : Ivan Cherednik
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 41,6 Mb
Release : 2002-12-19
Category : Mathematics
ISBN : 3540002243

Get Book

Iwahori-Hecke Algebras and Their Representation Theory by Ivan Cherednik Pdf

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. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 52,5 Mb
Release : 2011-10-23
Category : Mathematics
ISBN : 9781461407768

Get Book

Representation Theory of Finite Groups by Benjamin Steinberg Pdf

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Author : Gustave Choquet
Publisher : Unknown
Page : 7 pages
File Size : 55,9 Mb
Release : 1969
Category : Mathematical analysis
ISBN : 0805369635

Get Book

Lectures on Analysis by Gustave Choquet Pdf

Author : Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 55,5 Mb
Release : 2017-12-15
Category : Algebraic varieties
ISBN : 9781470435745

Get Book

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.

Author : Ken Brown,Ken R. Goodearl
Publisher : Birkhäuser
Page : 339 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882057

Get Book

Lectures on Algebraic Quantum Groups by Ken Brown,Ken R. Goodearl Pdf

This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Author : Adriano M. Garsia,Ömer Eğecioğlu
Publisher : Springer
Page : 232 pages
File Size : 51,6 Mb
Release : 2020-10-07
Category : Mathematics
ISBN : 3030583724

Get Book

Lectures in Algebraic Combinatorics by Adriano M. Garsia,Ömer Eğecioğlu Pdf

Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.

Author : Aleksandr Aleksandrovich Kirillov
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 48,5 Mb
Release : 2004
Category : Lie groups
ISBN : 9780821835302

Get Book

Lectures on the Orbit Method by Aleksandr Aleksandrovich Kirillov Pdf

Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 53,6 Mb
Release : 2006-11-21
Category : Mathematics
ISBN : 9780821842294

Get Book

Character Theory of Finite Groups by I. Martin Isaacs Pdf

Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.