Klimyk, A. U. (Anatoliĭ Ulʹi︠a︡novich) 1939Overview
Most widely held works by
A. U Klimyk
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
24 editions published between 1991 and 2011 in English and held by 313 WorldCat member libraries worldwide The present book is a continuation of the threevolume 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 hharmonic 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 ClebschGordan 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
Quantum groups and their representations
by A. U Klimyk
(
Book
)
10 editions published between 1997 and 2012 in English and held by 271 WorldCat member libraries worldwide This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but wellchosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and qdeformed algebras (qoscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed
Problems of modern quantum field theory : invited lectures of the Spring School, held in Alushta USSR, April 24May 5, 1989
by A. A Belavin
(
Book
)
3 editions published in 1989 in English and held by 156 WorldCat member libraries worldwide "This volume contains the invited lectures of a school on modern quantum field theory held at Alushta, USSR, in May 1989. The development of this subject, including string theories attempting to model elementary particles, is closely interwoven with modern mathematical physics. The lectures presented by experts in the field provide an overview of the research pursued in different branches of this rapidly evolving field and draw attention to particular interconnections and problems. Topics covered include: geometrical quantization and finite size effects in conformal field theory; quasiHopf, KacMoody current and Lie superalgebras; quantum groups; WessZuminoWitten models; NizhnikZamolodchikov equations; nonarchimedian strings; string dynamics; KdV and KP (super) equations and calculations on (super) riemannian surfaces; 2d Ising model and 2d electron motion on surfaces in external magnetic fields."Publisher's web site
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
9 editions published in 1991 in English and held by 24 WorldCat member libraries worldwide 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 selfcontained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory. For research mathematicians, physicists and engineers
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
4 editions published between 1992 and 2011 in English and held by 24 WorldCat member libraries worldwide 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 qanalogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semisimple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fandTsetlin basis, and, finally, modular forms, thetafunctions 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%
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
4 editions published between 1993 and 2011 in English and held by 21 WorldCat member libraries worldwide This is the second 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 special functions and orthogonal polynomials (Legendre, Gegenbauer, Jacobi, Laguerre, Bessel and others) which are related to the class 1 representations of various groups. The tree method for the construction of bases for representation spaces is given. `Continuous' bases in the spaces of functions on hyperboloids and cones and corresponding Poisson kernels are found. Also considered are the properties of the qanalogs of classical orthogonal polynomials, related to representations of the Chevalley groups and of special functions connected with fields of padic numbers. Much of the material included appears in book form for the first time and many of the topics are presented in a novel way. This volume will be of great interest to specialists in group representations, special functions, differential equations with partial derivatives and harmonic anlysis. Subscribers to the complete set of three volumes will be entitled to a discount of 15%
Simplest Lie groups, special functions and integral transforms
by N. I︠A︡ Vilenkin
(
Book
)
2 editions published in 1991 in English and held by 10 WorldCat member libraries worldwide
Classical and quantum groups and special functions
by N. I︠A︡ Vilenkin
(
Book
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3 editions published between 1991 and 1992 in English and held by 9 WorldCat member libraries worldwide
Matrichnye ėlementy i koėffit︠s︡ienty KlebshaGordana predstavleniĭ grupp
by A. U Klimyk
(
Book
)
2 editions published in 1979 in Russian and held by 8 WorldCat member libraries worldwide
Matričnye ėlementy i koėfficienty KlebšaGordana predstavlenij grupp
by A. U Klimyk
(
Book
)
4 editions published in 1979 in Russian and Ukrainian and held by 8 WorldCat member libraries worldwide
Class I representations, special functions, and integral transforms
by N. I︠A︡ Vilenkin
(
Book
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3 editions published between 1991 and 1993 in English and held by 8 WorldCat member libraries worldwide
Matematychni osnovy teoriï symetriĭ
by P. I Holod
(
Book
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1 edition published in 1992 in Ukrainian and held by 4 WorldCat member libraries worldwide
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
1 edition published in 1992 in English and held by 3 WorldCat member libraries worldwide
Vychislitelʹnye metody v teorii predstavleniĭ grupp
by A. U Klimyk
(
Book
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1 edition published in 1986 in Russian and held by 3 WorldCat member libraries worldwide
Representations of current algebra with structural constants of rotation group
by A. U Klimyk
(
Book
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1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Representation of Lie groups and special functions
by N. I︠A︡ Vilenkin
(
Book
)
1 edition published in 1995 in English and held by 2 WorldCat member libraries worldwide
Vyčislitelʹnye metody v teorii predstavlenij grupp
by A. U Klimyk
(
Book
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2 editions published in 1986 in Russian and Ukrainian and held by 2 WorldCat member libraries worldwide
Teorija predstavlenij grupp i ee priloženija
by A. O Barut
(
Book
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1 edition published in 1980 in Russian and held by 1 WorldCat member library worldwide
Recent advances
by Naum Ja Vilenkin
(
Book
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1 edition published in 1995 in Undetermined and held by 1 WorldCat member library worldwide more
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Associated Subjects
Algebra of currents Functions, Special Group theory Harmonic analysis Integral transforms Lie groups Mathematical physics Mathematics Matrices Physics Quantum field theory Quantum groups Quantum theory Representations of algebras Representations of groups Representations of Lie groups Representations of quantum groups Rotation groups Symmetry groups Topological groups

Alternative Names
Klimyk, A. U.
Klimyk, Anatoli.
Klimyk Anatoli Ulianovitch 1939....
Klimyk, Anatoliǐ Ul'ianovich
Klimyk, Anatoliĭ Ulʹi︠a︡novich, 1939
Klimyk, Anatolij.
Klimyk, Anatolij Ul'janovič
Klimyk, Anatolij Ul'janovič. [t]
Klymyk Anatoli Uljanovich
Klymyk Anatoli Uljanovich, 1939
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