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Author : Miller
Publisher : Academic Press
ISBN 13 : 0080955517
Total Pages : 357 pages
Book Rating : 4.0/5 (89 download)
Download or read book Lie Theory and Special Functions written by Miller and published by Academic Press. This book was released on 1968 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie Theory and Special Functions
Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 9401728852
Total Pages : 518 pages
Book Rating : 4.4/5 (17 download)
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.
Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 940113538X
Total Pages : 635 pages
Book Rating : 4.4/5 (11 download)
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.
Author : Willard Miller
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (68 download)
Download or read book Lie Theory and Special Functions written by Willard Miller and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Willard Miller
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (959 download)
Download or read book Lie Theory and Special Functions Special Functions written by Willard Miller and published by . This book was released on 1968 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821815724
Total Pages : 613 pages
Book Rating : 4.8/5 (157 download)
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.
Author : Naum I͡Akovlevich Vilenkin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886526
Total Pages : 628 pages
Book Rating : 4.8/5 (865 download)
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:
Author : Jean Dieudonné
Publisher : American Mathematical Soc.
ISBN 13 : 0821816926
Total Pages : 65 pages
Book Rating : 4.8/5 (218 download)
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:
Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 940172881X
Total Pages : 651 pages
Book Rating : 4.4/5 (17 download)
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%.
Author : Dwivedi Ravi
Publisher :
ISBN 13 : 9784569246321
Total Pages : 0 pages
Book Rating : 4.2/5 (463 download)
Download or read book Lie Theory Matrix Theory and Special Functions written by Dwivedi Ravi and published by . This book was released on 2022-11-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we give a brief review of the theory of special functions, special matrix functions and representation theory of Lie algebras that will be needed in the subsequent chapters. The theory of special functions has been enriched by the works of Euler, Gauss, Kummer, Riemann and Ramanujan, to name a few. For a detailed study of the subject, we refer to Bailey [5], Erdelyi, Magnus, Oberhettinger and Tricomi [18], Rainville [64], Slater [75], Exton [20]-[22], Srivastava and Manocha [80], Srivastava and Karlsson [81], Gasper and Rahman [28] and Andrews, Askey and Roy [3].
Author : Willard Miller
Publisher : American Mathematical Soc.
ISBN 13 : 0821812505
Total Pages : 51 pages
Book Rating : 4.8/5 (218 download)
Download or read book On Lie Algebras and Some Special Functions of Mathematical Physics written by Willard Miller and published by American Mathematical Soc.. This book was released on 1964 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Willard Miller (Jr.)
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.:/5 (472 download)
Download or read book Lie Theory and Special Functions written by Willard Miller (Jr.) and published by . This book was released on 1968 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.M. Mathai
Publisher : Springer Science & Business Media
ISBN 13 : 0387758941
Total Pages : 480 pages
Book Rating : 4.3/5 (877 download)
Download or read book Special Functions for Applied Scientists written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2008-02-13 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.
Author : Vladimir Dobrev
Publisher : Springer Nature
ISBN 13 : 9811577757
Total Pages : 552 pages
Book Rating : 4.8/5 (115 download)
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author : Claude Chevalley
Publisher : Princeton University Press
ISBN 13 : 9780691049908
Total Pages : 234 pages
Book Rating : 4.0/5 (499 download)
Download or read book Theory of Lie Groups written by Claude Chevalley and published by Princeton University Press. This book was released on 2000-01-10 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.
Author : Claudio Procesi
Publisher : Springer Science & Business Media
ISBN 13 : 0387289291
Total Pages : 616 pages
Book Rating : 4.3/5 (872 download)
Download or read book Lie Groups written by Claudio Procesi and published by Springer Science & Business Media. This book was released on 2007-10-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. By covering sufficient background material, the book is made accessible to a reader with a relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. This unique exposition is suitable for a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.
