Representations of the Infinite Symmetric Group
Title | Representations of the Infinite Symmetric Group PDF eBook |
Author | Alexei Borodin |
Publisher | Cambridge University Press |
Pages | 169 |
Release | 2017 |
Genre | Mathematics |
ISBN | 1107175550 |
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize
Title | Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize PDF eBook |
Author | Sergei Vasilʹevich Kerov |
Publisher | American Mathematical Soc. |
Pages | 224 |
Release | |
Genre | Mathematics |
ISBN | 9780821889633 |
This book reproduces the doctoral thesis written by a remarkable mathematician, Sergei V. Kerov. His untimely death at age 54 left the mathematical community with an extensive body of work and this one-of-a-kind monograph. Here, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on an important topic of current research. Asymptotic representation theory of symmetric groups deals with problems of two types: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group. The author contributed significantly in the development of both directions. His book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram. He also studies stochastic properties of the deviations of random diagrams from the limiting curve. Among the problems of the second type, Kerov studies an important problem of computing irreducible characters of the infinite symmetric group. This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams. In turn, this construction provides a completely new description of the relation between the classical moment problems of Hausdorff and Markov. The book is suitable for graduate students and research mathematicians interested in representation theory and combinatorics.
Asymptotic Representation Theory of the Symmetric Group and Its Applications in Analysis
Title | Asymptotic Representation Theory of the Symmetric Group and Its Applications in Analysis PDF eBook |
Author | Sergei Vasilʹevich Kerov |
Publisher | |
Pages | |
Release | 2003 |
Genre | Representations of groups |
ISBN | 9781470446437 |
Asymptotic representation theory of symmetric groups deals with two types of problems: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group. The author contributed significantly in the development of problems of both types, and his book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation, and the limiting shape of a.
Representation Theory of Symmetric Groups
Title | Representation Theory of Symmetric Groups PDF eBook |
Author | Pierre-Loic Meliot |
Publisher | CRC Press |
Pages | 666 |
Release | 2017-05-12 |
Genre | Mathematics |
ISBN | 1498719139 |
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 Course in Finite Group Representation Theory
Title | A Course in Finite Group Representation Theory PDF eBook |
Author | Peter Webb |
Publisher | Cambridge University Press |
Pages | 339 |
Release | 2016-08-19 |
Genre | Mathematics |
ISBN | 1107162394 |
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Representation Theory of Finite Groups
Title | Representation Theory of Finite Groups PDF eBook |
Author | Benjamin Steinberg |
Publisher | Springer Science & Business Media |
Pages | 166 |
Release | 2011-10-23 |
Genre | Mathematics |
ISBN | 1461407761 |
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.
Representing Finite Groups
Title | Representing Finite Groups PDF eBook |
Author | Ambar N. Sengupta |
Publisher | Springer Science & Business Media |
Pages | 383 |
Release | 2011-12-09 |
Genre | Mathematics |
ISBN | 1461412315 |
This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful. A separate solutions manual is available for instructors.