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Theory of Group Representations and Applications

1986-11-01 Mathematics
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Release : 1986-11-01
Genre : Mathematics
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Book Rating : 876/5 ( reviews)

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Book Synopsis Theory of Group Representations and Applications by : A Barut

Download or read book Theory of Group Representations and Applications written by A Barut. This book was released on 1986-11-01. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy

An Introduction to the Representation Theory of Groups

2014-08-28 Mathematics
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Release : 2014-08-28
Genre : Mathematics
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Book Rating : 666/5 ( reviews)

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Book Synopsis An Introduction to the Representation Theory of Groups by : Emmanuel Kowalski

Download or read book An Introduction to the Representation Theory of Groups written by Emmanuel Kowalski. This book was released on 2014-08-28. Available in PDF, EPUB and Kindle. Book excerpt: Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.

Representation Theory of Finite Groups

2011-10-23 Mathematics
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Release : 2011-10-23
Genre : Mathematics
Kind : eBook
Book Rating : 761/5 ( reviews)

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Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg

Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg. This book was released on 2011-10-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize

Mathematics
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Genre : Mathematics
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Book Rating : 633/5 ( reviews)

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Book Synopsis Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize by : Sergei Vasilʹevich Kerov

Download or read book Asimptoti?eskaja teorija predstavlenija simmetri?eskoj gruppyi ee primenenija v analize written by Sergei Vasilʹevich Kerov. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graphs on Surfaces and Their Applications

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
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Book Rating : 611/5 ( reviews)

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Book Synopsis Graphs on Surfaces and Their Applications by : Sergei K. Lando

Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

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