Noncompact Lie Groups And Some Of Their Applications

Author : Elizabeth A. Tanner,R. Wilson
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401110785

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Noncompact Lie Groups and Some of Their Applications by Elizabeth A. Tanner,R. Wilson Pdf

During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.

Author : Daniel Bump
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 41,9 Mb
Release : 2013-10-01
Category : Mathematics
ISBN : 9781461480242

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Lie Groups by Daniel Bump Pdf

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.

Author : Robert Gilmore
Publisher : Courier Corporation
Page : 610 pages
File Size : 45,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131566

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Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore Pdf

This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 51,8 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Author : Robert S. Doran
Publisher : American Mathematical Soc.
Page : 568 pages
File Size : 41,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821811979

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The Mathematical Legacy of Harish-Chandra by Robert S. Doran Pdf

Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, "Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers. The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, "Some Recollections of Harish-Chandra", by A. Borel, and "Harish-Chandra's c-Function: A Mathematical Jewel", by S. Helgason. In addition, an expository paper, "An Elementary Introduction to Harish-Chandra's Work", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis.

Author : Jean Marion,Herbert Heyer
Publisher : World Scientific
Page : 410 pages
File Size : 42,6 Mb
Release : 1998-10-30
Category : Electronic
ISBN : 9789814544849

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Analysis On Infinite-dimensional Lie Groups And Algebras - Proceedings Of The International Colloquium by Jean Marion,Herbert Heyer Pdf

This proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.

Author : Tadeusz Lulek,Wojciech Florek,Stanislaw Walcerz
Publisher : World Scientific
Page : 526 pages
File Size : 48,5 Mb
Release : 1995-03-29
Category : Electronic
ISBN : 9789814550024

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Symmetry And Structural Properties Of Condensed Matter, Proceedings Of The 3rd International School On Theoretical Physics by Tadeusz Lulek,Wojciech Florek,Stanislaw Walcerz Pdf

This volume reviews some selected problems in solid state physics with an emphasis on adequate mathematical tools. The three main subjects are magnetic structures and neutron scattering; Berry phases and energy bands in solids (symmetry, analicity, Hofstadter butterfly, van Hove singularities); and quasicrystals, finite systems, and group action on sets (unitary group approach, Schur functions). Software presentations are included as a separate part.

Author : Peter Schneider
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 48,7 Mb
Release : 2011-06-11
Category : Mathematics
ISBN : 9783642211478

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p-Adic Lie Groups by Peter Schneider Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 812 pages
File Size : 44,7 Mb
Release : 2002
Category : Lie algebras
ISBN : 3764342595

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Lie Groups Beyond an Introduction by Anonim Pdf

Author : Hossein Abbaspour,Martin Moskowitz
Publisher : World Scientific Publishing Company
Page : 444 pages
File Size : 51,6 Mb
Release : 2007-09-21
Category : Mathematics
ISBN : 9789813101562

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Basic Lie Theory by Hossein Abbaspour,Martin Moskowitz Pdf

This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or on lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped. The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.

Author : Z. Horv th,L. Palla
Publisher : World Scientific
Page : 471 pages
File Size : 53,5 Mb
Release : 2001
Category : Science
ISBN : 9789810246495

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Non-perturbative QFT Methods and Their Applications by Z. Horv th,L. Palla Pdf

http://www.worldscientific.com/worldscibooks/10.1142/4727

Author : Z. Horv th,L. Palla
Publisher : World Scientific
Page : 474 pages
File Size : 47,5 Mb
Release : 2001
Category : Science
ISBN : 9812799966

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Nonperturbative Quantum-field-theoretic Methods and Their Applications by Z. Horv th,L. Palla Pdf

Contents: Conformal Boundary Conditions OCo and What They Teach Us (V B Petkova & J-B Zuber); A Physical Basis for the Entropy of the AdS 3 Black Hole (S Fernando & F Mansouri); Spinon Formulation of the Kondo Problem (A Klmper & J R Reyes-Martinez); Boundary Integrable Quantum Field Theories (P Dorey); Finite Size Effects in Integrable Quantum Field Theories (F Ravanini); Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.); Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.); Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich); Phase Transitions in Non-Hermitean Matrix Models and the OC Single RingOCO Theorem (J Feinberg et al.); Unraveling the Mystery of Flavor (A Falk); The Nahm Transformation on R 2 X T 2 (C Ford); A 2D Integrable Axion Model and Target Space Duality (P Forgics); Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker); and other papers. Readership: Theoretical, mathematical and high energy physicists."

Author : Zalan Horvath,Laszlo Palla
Publisher : World Scientific
Page : 471 pages
File Size : 47,8 Mb
Release : 2001-05-18
Category : Science
ISBN : 9789814490832

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Non-perturbative Qft Methods And Their Applications, Procs Of The Johns Hopkins Workshop On Current Problems In Particle Theory 24 by Zalan Horvath,Laszlo Palla Pdf

Contents:Conformal Boundary Conditions — and What They Teach Us (V B Petkova & J-B Zuber)A Physical Basis for the Entropy of the AdS3 Black Hole (S Fernando & F Mansouri)Spinon Formulation of the Kondo Problem (A Klümper & J R Reyes-Martinez)Boundary Integrable Quantum Field Theories (P Dorey)Finite Size Effects in Integrable Quantum Field Theories (F Ravanini)Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.)Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.)Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich)Phase Transitions in Non-Hermitean Matrix Models and the “Single Ring” Theorem (J Feinberg et al.)Unraveling the Mystery of Flavor (A Falk)The Nahm Transformation on R2 X T2 (C Ford)A 2D Integrable Axion Model and Target Space Duality (P Forgács)Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker)and other papers Readership: Theoretical, mathematical and high energy physicists. Keywords:

Author : Christian Voigt,Robert Yuncken
Publisher : Springer Nature
Page : 382 pages
File Size : 49,9 Mb
Release : 2020-09-24
Category : Mathematics
ISBN : 9783030524630

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Complex Semisimple Quantum Groups and Representation Theory by Christian Voigt,Robert Yuncken Pdf

This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.

Author : Juan Tirao,David Vogan,Joe Wolf
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241621

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Geometry and Representation Theory of Real and p-adic groups by Juan Tirao,David Vogan,Joe Wolf Pdf

The representation theory of Lie groups plays a central role in both clas sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.