Asymptotic Representation Theory Of The Symmetric Group And Its Applications In Analysis
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Author | : Sergei Vasilʹevich Kerov |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821889633 |
Download Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize Book in PDF, Epub and Kindle
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.
Author | : Sergei Vasilʹevich Kerov |
Publisher | : |
Total Pages | : |
Release | : 2003 |
Genre | : Representations of groups |
ISBN | : 9781470446437 |
Download Asymptotic Representation Theory of the Symmetric Group and Its Applications in Analysis Book in PDF, Epub and Kindle
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.
Author | : Pierre-Loic Meliot |
Publisher | : CRC Press |
Total Pages | : 666 |
Release | : 2017-05-12 |
Genre | : Mathematics |
ISBN | : 1498719139 |
Download Representation Theory of Symmetric Groups Book in PDF, Epub and Kindle
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.
Author | : European Mathematical Summer School (2001 : St. Petersburg) |
Publisher | : Springer Science & Business Media |
Total Pages | : 245 |
Release | : 2003 |
Genre | : Asymptotic expansions |
ISBN | : 3540403124 |
Download Asymptotic Combinatorics with Applications to Mathematical Physics Book in PDF, Epub and Kindle
At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.
Author | : Alexei Borodin |
Publisher | : Cambridge University Press |
Total Pages | : 169 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 1107175550 |
Download Representations of the Infinite Symmetric Group Book in PDF, Epub and Kindle
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Author | : Gordon Douglas James |
Publisher | : Westview Press |
Total Pages | : 554 |
Release | : 1981 |
Genre | : Mathematics |
ISBN | : |
Download The Representation Theory of the Symmetric Group Book in PDF, Epub and Kindle
Author | : Gilbert de Beauregard Robinson |
Publisher | : Edinburgh : University Press |
Total Pages | : 218 |
Release | : 1961 |
Genre | : Group theory |
ISBN | : |
Download Representation Theory of the Symmetric Group Book in PDF, Epub and Kindle
Author | : Dmitriĭ Petrovich Zhelobenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 456 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821889671 |
Download Principal Structures and Methods of Representation Theory Book in PDF, Epub and Kindle
The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups,along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Liealgebras and Lie groups, Banach algebras, and quantum groups. This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading. Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.
Author | : Александр Яковлевич Хелемский |
Publisher | : American Mathematical Soc. |
Total Pages | : 496 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821889695 |
Download Lectures and Exercises on Functional Analysis Book in PDF, Epub and Kindle
The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.
Author | : |
Publisher | : |
Total Pages | : 510 |
Release | : 1984 |
Genre | : Representations of groups |
ISBN | : 9781107340732 |
Download The Representation Theory of the Symmetric Group Book in PDF, Epub and Kindle