Complex Semisimple Quantum Groups and Representation Theory, Voigt Christian, Yuncken Robert
Автор: Chriss, Neil Ginzburg, Victor Название: Representation theory and complex geometry ISBN: 0817649379 ISBN-13(EAN): 9780817649371 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. This is the only available introduction to geometric representation theory...it has already proved successful in introducing a new generation to the subject."
Автор: Hayashi Masahito Название: Group Representation for Quantum Theory ISBN: 3319831593 ISBN-13(EAN): 9783319831596 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explains the group representation theory for quantum theory in the language of quantum theory.
Автор: Enrico Casadio Tarabusi; Michael Cowling; Andrea D Название: Representation Theory and Complex Analysis ISBN: 3540768912 ISBN-13(EAN): 9783540768913 Издательство: Springer Рейтинг: Цена: 6981.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability.
Автор: Gregori A. Margulis Название: Discrete Subgroups of Semisimple Lie Groups ISBN: 3642057217 ISBN-13(EAN): 9783642057212 Издательство: Springer Рейтинг: Цена: 25149.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. The author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature.
Автор: Louis Boutet de Monvel; Giuseppe Zampieri; Andrea Название: D-modules, Representation Theory, and Quantum Groups ISBN: 3540574980 ISBN-13(EAN): 9783540574989 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains a series of lectures presented at the 2nd Session of the Centro Internazionale Matematica Estivo (CIME), held in Venezia, Italy in June 1992. It includes discussion of quantum groups and the index theorems for R-constructible sheaves and for D-modules.
Описание: A self-contained treatment of the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The book functions as both a useful reference for researchers, and a graduate textbook with plenty of examples and several exercises.
Автор: Hayashi Название: Group Representation for Quantum Theory ISBN: 3319449044 ISBN-13(EAN): 9783319449043 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory.Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions.
Автор: Vergados John D Название: Group And Representation Theory ISBN: 9813202440 ISBN-13(EAN): 9789813202443 Издательство: World Scientific Publishing Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.
This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elements of the algebra on uniquely specified highest weight states. Alternatively these representations can be described in terms of tensors labeled by the Young tableaux associated with the discrete symmetry Sn. The connection between the Young tableaux and the Dynkin weights is also discussed. It is also shown that in many physical systems the quantum numbers needed to specify the physical states involve not only the highest symmetry but also a number of sub-symmetries contained in them. This leads to the study of the role of subalgebras and in particular the possible maximal subalgebras. In many applications the physical system can be considered as composed of subsystems obeying a given symmetry. In such cases the reduction of the Kronecker product of irreducible representations of classical and special algebras becomes relevant and is discussed in some detail. The method of obtaining the relevant Clebsch-Gordan (C-G) coefficients for such algebras is discussed and some relevant algorithms are provided. In some simple cases suitable numerical tables of C-G are also included.
The above exposition contains many examples, both as illustrations of the main ideas as well as well motivated applications. To this end two appendices of 51 pages -- 11 tables in Appendix A, summarizing the material discussed in the main text and 39 tables in Appendix B containing results of more sophisticated examples are supplied. Reference to the tables is given in the main text and a guide to the appropriate section of the main text is given in the tables.
Автор: Vladimir K. Dobrev Название: Noncompact Semisimple Lie Algebras and Groups ISBN: 311043542X ISBN-13(EAN): 9783110435429 Издательство: Walter de Gruyter Цена: 24165.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrodinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents:IntroductionLie Algebras and GroupsReal Semisimple Lie AlgebrasInvariant Differential OperatorsCase of the Anti-de Sitter GroupConformal Case in 4DKazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant EquationsInvariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie AlgebrasMultilinear Invariant Differential Operators from New Generalized Verma ModulesBibliographyAuthor IndexSubject Index
Автор: Glen Jones; Jean-Pierre Serre Название: Complex Semisimple Lie Algebras ISBN: 0387965696 ISBN-13(EAN): 9780387965697 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These are indicated by an asterisk, and the proofs can be found in Bourbaki, Groupes et Algebres de Lie, Paris, Hermann, 1960-1975, Chapters IV-VIII. A final chapter shows, without proof, how to pass from Lie algebras to Lie groups (complex-and also compact).
Автор: Glen Jones; Jean-Pierre Serre Название: Complex Semisimple Lie Algebras ISBN: 364263222X ISBN-13(EAN): 9783642632228 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These short notes, already well-known in their original French edition, present the basic theory of semisimple Lie algebras over the complex numbers. The last chapter discusses the connection between Lie algebras, complex groups and compact groups.
Автор: Varadarajan V. S. Название: An Introduction to Harmonic Analysis on Semisimple Lie Groups ISBN: 0521663628 ISBN-13(EAN): 9780521663625 Издательство: Cambridge Academ Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Now in paperback, this graduate-level textbook introduces the representation theory of semi-simple Lie groups. Containing appendices sketching some basic topics with a comprehensive guide to further reading, it is suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic.
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