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Representation of Lie groups and special functions recent advances by N. IНЎA Vilenkin

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Published by Kluwer Academic Publishers in Dordrecht, Boston .
Written in English

Subjects:

  • Representations of groups,
  • Lie groups,
  • Functions, Special,
  • Integral transforms

Book details:

Edition Notes

Includes bibliographical references (p. 463-487) and index.

Statementby N.Ja. Vilenkin and A.U. Klimyk ; [translated from Russian by V.A. Groza and A.A. Groza].
SeriesMathematics and its applications ;, v. 316, Mathematics and its applications (Kluwer Academic Publishers) ;, v. 316.
ContributionsKlimyk, A. U. 1939-
Classifications
LC ClassificationsQA176 .V55 1995
The Physical Object
Paginationxvi, 497 p. ;
Number of Pages497
ID Numbers
Open LibraryOL833422M
ISBN 100792332105
LC Control Number95108075

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Representation of Lie Groups and Special Functions Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.   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. special functions. Speci cally, it was discovered that many of the special functions are (1) speci c matrix elements of matrix representations of Lie groups, and (2) basis functions of operator representations of Lie algebras. By viewing the special func-tions in this way, it is possible to derive many of their properties that were originally.

$, ISBN ; Vol. 3: Classical and quantum groups and special functions, vol. 75, , xx+ pp., $, ISBN X Review by Erik Koelink and Tom H. Koornwinder The book under review deals with the interplay between two branches of mathematics, namely representation theory of groups and the theory of special functions. In our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications.. The term is defined by consensus, and thus lacks a general formal definition, but the List of mathematical functions contains functions that are commonly accepted as special. Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.

  Differential properties of spherical functions on Lie groups 40 45; Spherical functions on semisimple Lie groups 42 47; More on SL(2, R) 45 50; Automorphic functions 53 58; Groups of isometries and Bessel functions 55 60; Other special functions 58 63; References 59 64; Back Cover Back Cover1 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. User Review - Flag as inappropriate 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 s: 1. book [27] for the representation theory of compact Lie groups and semisimple Lie algberas, Serre’s books [31] and [30] for a very different approach to many of the same topics (Lie groups, Lie algebras, and their representations), and the book [8] of Demazure-Gabriel for more about algebraic groups.