This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.
The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.
Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.
Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Автор: N. G. Basov Название: Problems in the General Theory of Relativity and Theory of Group Representations ISBN: 1468406787 ISBN-13(EAN): 9781468406788 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This collection contains survey articles dealing with the following topics: The Mach principle and its role in the general theory of relativity, the modern conception of the vacuum, new methods in the theory of Lie group representations, the coherent state method and its applica- tion to physical problems, and the Newman-Penrose method and its application to problems in general relativity theory. v CONTENTS On the Problem of Singularity in the De Sitter Model . . . . . . . . . . . . . . . . . . . . . . . . . . 1 v. K. Mal'tsev and M. A. Markov On the Integral Formulation of the Mach Principle in a Conformally Flat Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. 9 v. K. Mal'tsev and M. A. Markov Canonical Transformations and the Theory of Representations of Lie Groups . -------- 25 A. N. Leznov, I. A. Malkin, and V. I. Man'ko The Newman-Penrose Method in the Theory of General Relativity. - - - - - - - - - - - -- - 73 - - V. P. Frolov vii ON THE PROBLEM OF SINGULARITY IN THE DE SITTER MODEL V. K. Mal'tsev and M. A. Markov --- The de Sitter solution in no way corresponds to the case of a world without matter, but corresponds rather to a world in which all matter is concentrated on the surface r = IT /2 which could proba bly be proved by taking the limit from a volume distri bution of matter to a surface distribution 1].
Автор: Konno Hitoshi Название: Elliptic Quantum Groups: Representations and Related Geometry ISBN: 9811573867 ISBN-13(EAN): 9789811573866 Издательство: Springer Рейтинг: Цена: 60550.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation.
Автор: Melnikov Название: Space Group Representations ISBN: 3031139909 ISBN-13(EAN): 9783031139901 Издательство: Springer Рейтинг: Цена: 149060.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.
Автор: Kobayashi, Toshiyuki Speh, Birgit Название: Symmetry breaking for representations of rank one orthogonal groups ii ISBN: 9811329001 ISBN-13(EAN): 9789811329005 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.
The study of symmetry breaking operators (intertwining operators for restriction) is an important and very active research area in modern representation theory, which also interacts with various fields in mathematics and theoretical physics ranging from number theory to differential geometry and quantum mechanics.
The first author initiated a program of the general study of symmetry breaking operators. The present book pursues the program by introducing new ideas and techniques, giving a systematic and detailed treatment in the case of orthogonal groups of real rank one, which will serve as models for further research in other settings.
In connection to automorphic forms, this work includes a proof for a multiplicity conjecture by Gross and Prasad for tempered principal series representations in the case (SO(n + 1, 1), SO(n, 1)). The authors propose a further multiplicity conjecture for nontempered representations.
Viewed from differential geometry, this seminal work accomplishes the classification of all conformally covariant operators transforming differential forms on a Riemanniann manifold X to those on a submanifold in the model space (X, Y) = (Sn, Sn-1). Functional equations and explicit formul? of these operators are also established.
This book offers a self-contained and inspiring introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in representation theory, automorphic forms, differential geometry, and theoretical physics.
Автор: Roe Goodman; Nolan R. Wallach Название: Symmetry, Representations, and Invariants ISBN: 1441927298 ISBN-13(EAN): 9781441927293 Издательство: Springer Рейтинг: Цена: 55850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book is a significant reworking of an earlier work by the authors. It offers a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that includes a broader range of applications.
Автор: Woit, Peter Название: Quantum theory, groups and representations ISBN: 3319878352 ISBN-13(EAN): 9783319878355 Издательство: Springer Рейтинг: Цена: 74530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject.
Автор: Philipp Fleig, Henrik P. A. Gustafsson, Axel Kleinschmidt, Daniel Persson Название: Eisenstein Series and Automorphic Representations: With Applications in String Theory ISBN: 1107189926 ISBN-13(EAN): 9781107189928 Издательство: Cambridge Academ Рейтинг: Цена: 88710.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Aimed at advanced students and active researchers in mathematics or theoretical physics, this book provides a detailed exposition of automorphic forms and representations, from the basics up to cutting-edge research topics at the interface between number theory and string theory.
Автор: Kenji Iohara; Sophie Morier-Genoud; Bertrand R?my Название: Symmetries, Integrable Systems and Representations ISBN: 1447148622 ISBN-13(EAN): 9781447148623 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This volume is the result of two international workshops; Infinite Analysis 11 - Frontier of Integrability - held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Universit Claude Bernard Lyon 1, France in December 13th to 16th, 2011.
Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.
Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Автор: Vladimir I. Arnold; Alexander B. Givental; Boris K Название: Vladimir I. Arnold - Collected Works ISBN: 3642261329 ISBN-13(EAN): 9783642261329 Издательство: Springer Рейтинг: Цена: 167700.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.
Казахстан, 010000 г. Астана, проспект Туран 43/5, НП2 (офис 2) ТОО "Логобук" Тел:+7 707 857-29-98 ,+7(7172) 65-23-70 www.logobook.kz
