Compact Lie Groups
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Compact Lie Groups
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Author : Mark R. Sepanski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-19
Compact Lie Groups written by Mark R. Sepanski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-19 with Mathematics categories.
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.
Representations Of Compact Lie Groups
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Author : T. Bröcker
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-02
Representations Of Compact Lie Groups written by T. Bröcker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-02 with Mathematics categories.
This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.
Compact Lie Groups And Their Representations
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Author : Dmitriĭ Petrovich Zhelobenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1973-01-01
Compact Lie Groups And Their Representations written by Dmitriĭ Petrovich Zhelobenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-01-01 with Mathematics categories.
Lie Groups
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Author : Daniel Bump
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-01
Lie Groups written by Daniel Bump and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Mathematics categories.
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
Lie Groups Lie Algebras And Representations
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Author : Brian Hall
language : en
Publisher: Springer
Release Date : 2015-05-11
Lie Groups Lie Algebras And Representations written by Brian Hall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-11 with Mathematics categories.
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Introduction To Compact Lie Groups
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Author : Howard D Fegan
language : en
Publisher: World Scientific Publishing Company
Release Date : 1991-07-30
Introduction To Compact Lie Groups written by Howard D Fegan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-07-30 with categories.
There are two approaches to compact lie groups: by computation as matrices or theoretically as manifolds with a group structure. The great appeal of this book is the blending of these two approaches. The theoretical results are illustrated by computations and the theory provides a commentary on the computational work. Indeed, there are extensive computations of the structure and representation theory for the classical groups SU(n), SO(n) and Sp(n). A second exciting feature is that the differential geometry of a compact Lie group, both the classical curvature studies and the more recent heat equation methods, are treated. A large number of formulas for the connection and curvature are conveniently gathered together.This book provides an excellent text for a first course in compact Lie groups.
Lie Groups
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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lie Groups written by J.J. Duistermaat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is devoted to an exposition of the theory of finite-dimensional Lie groups and Lie algebras, which is a beautiful and central topic in modern mathematics. At the end of the nineteenth century this theory came to life in the works of Sophus Lie. It had its origins in Lie's idea of applying Galois theory to differential equations and in Klein's "Erlanger Programm" of treat ing symmetry groups as the fundamental objects in geometry. Lie's approach to many problems of analysis and geometry was mainly local, that is, valid in local coordinate systems only. At the beginning of the twentieth century E. Cartan and Weyl began a systematic treatment of the global aspects of Lie's theory. Since then this theory has ramified tremendously and now, as the twentieth century is coming to a close, its concepts and methods pervade mathematics and theoretical physics. Despite the plethora of books devoted to Lie groups and Lie algebras we feel there is justification for a text that puts emphasis on Lie's principal idea, namely, geometry treated by a blend of algebra and analysis. Lie groups are geometrical objects whose structure can be described conveniently in terms of group actions and fiber bundles. Therefore our point of view is mainly differential geometrical. We have made no attempt to discuss systematically the theory of infinite-dimensional Lie groups and Lie algebras, which is cur rently an active area of research. We now give a short description of the contents of each chapter.
Representations Of Compact Lie Groups
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Author : T. Bröcker
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Representations Of Compact Lie Groups written by T. Bröcker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras, though mentioned occasionally, are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago. Prerequisites to the book are standard linear algebra and analysis, including Stokes' theorem for manifolds. The book can be read by German students in their third year, or by first-year graduate students in the United States. Generally speaking the book should be useful for mathematicians with geometric interests and, we hope, for physicists. At the end of each section the reader will find a set of exercises. These vary in character:Some ask the reader to verify statements used in the text, some contain additional information, and some present examples and counter examples. We advise the reader at least to read through the exercises.
P Adic Lie Groups
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Author : Peter Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-11
P Adic Lie Groups written by Peter Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-11 with Mathematics categories.
Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.