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Special Functions And The Theory Of Group Representations
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Book Synopsis Special Functions and the Theory of Group Representations by : Naum I͡Akovlevich Vilenkin
Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1978 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Functions and the Theory of Group Representations by : Naum I͡Akovlevich Vilenkin
Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.
Book Synopsis Representation of Lie Groups and Special Functions by : N.Ja. Vilenkin
Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given. The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers.
Book Synopsis Representation of Lie Groups and Special Functions by : N.Ja. Vilenkin
Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.
Book Synopsis Special Functions and the Theory of Group Representations by : Naum Ja Vilenkin
Download or read book Special Functions and the Theory of Group Representations written by Naum Ja Vilenkin and published by . This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Functions and the Theory of Group Representations by :
Download or read book Special Functions and the Theory of Group Representations written by and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Functions and the Theory of Group Representations by : Naum Âkovlevič Vilenkin
Download or read book Special Functions and the Theory of Group Representations written by Naum Âkovlevič Vilenkin and published by . This book was released on 1988 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Functions and Linear Representations of Lie Groups by : Jean Dieudonné
Download or read book Special Functions and Linear Representations of Lie Groups written by Jean Dieudonné and published by American Mathematical Soc.. This book was released on 1980 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representation Theory and Noncommutative Harmonic Analysis II by : A.A. Kirillov
Download or read book Representation Theory and Noncommutative Harmonic Analysis II written by A.A. Kirillov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Book Synopsis Group Theory in Physics by : Wu-Ki Tung
Download or read book Group Theory in Physics written by Wu-Ki Tung and published by World Scientific. This book was released on 1985 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet.
Book Synopsis Special functions and the theory of group representations by : Naum Jakovlevič Vilenkin
Download or read book Special functions and the theory of group representations written by Naum Jakovlevič Vilenkin and published by . This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Group Characters and Matrix Representations of Groups by : Dudley Ernest Littlewood
Download or read book The Theory of Group Characters and Matrix Representations of Groups written by Dudley Ernest Littlewood and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding of beautiful classical results about group representations.
Book Synopsis Representation of Lie Groups and Special Functions by : N. Ja. Vilenkin
Download or read book Representation of Lie Groups and Special Functions written by N. Ja. Vilenkin and published by . This book was released on 2014-01-15 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Group Representations by : M.A. Naimark
Download or read book Theory of Group Representations written by M.A. Naimark and published by Springer. This book was released on 2011-11-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author's Preface to the Russian Edition This book is written for advanced students, for predoctoral graduate stu dents, and for professional scientists-mathematicians, physicists, and chemists-who desire to study the foundations of the theory of finite dimensional representations of groups. We suppose that the reader is familiar with linear algebra, with elementary mathematical analysis, and with the theory of analytic functions. All else that is needed for reading this book is set down in the book where it is needed or is provided for by references to standard texts. The first two chapters are devoted to the algebraic aspects of the theory of representations and to representations of finite groups. Later chapters take up the principal facts about representations of topological groups, as well as the theory of Lie groups and Lie algebras and their representations. We have arranged our material to help the reader to master first the easier parts of the theory and later the more difficult. In the author's opinion, however, it is algebra that lies at the heart of the whole theory. To keep the size of the book within reasonable bounds, we have limited ourselves to finite-dimensional representations. The author intends to devote another volume to a more general theory, which includes infinite dimensional representations.
Author :Naum I︠A︡kovlevich Vilenkin Publisher :Springer Science & Business Media ISBN 13 :9780792332107 Total Pages :528 pages Book Rating :4.3/5 (321 download)
Book Synopsis Representation of Lie Groups and Special Functions by : Naum I︠A︡kovlevich Vilenkin
Download or read book Representation of Lie Groups and Special Functions written by Naum I︠A︡kovlevich Vilenkin and published by Springer Science & Business Media. This book was released on 1995 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is a continuation of the three-volume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to Clebsch-Gordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics.
Book Synopsis Representation of Lie Groups and Special Functions by : N.Ja. Vilenkin
Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with q-analogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semi-simple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fand-Tsetlin basis, and, finally, modular forms, theta-functions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.
Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
