Affine Lie Algebras Weight Multiplicities And Branching Rules

Author : Sam Kass,R. V. Moody,J. Patera,R. Slansky
Publisher : Univ of California Press
Page : 312 pages
File Size : 53,6 Mb
Release : 1990-01-01
Category : Science
ISBN : 0520067681

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Affine Lie Algebras, Weight Multiplicities, and Branching Rules by Sam Kass,R. V. Moody,J. Patera,R. Slansky Pdf

00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 49,6 Mb
Release : 1990
Category : Electronic
ISBN : OCLC:634134732

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Affine Lie Algebras, Weight Multiplicities, and Branching Rules by Anonim Pdf

Author : Jang Soo Kim,Kyu-Hwan Lee,Se-jin Oh
Publisher : American Mathematical Society
Page : 100 pages
File Size : 51,9 Mb
Release : 2023-03-09
Category : Mathematics
ISBN : 9781470459949

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Weight Multiplicities and Young Tableaux Through Affine Crystals by Jang Soo Kim,Kyu-Hwan Lee,Se-jin Oh Pdf

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Author : Yvan Saint-Aubin,Luc Vinet
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461301196

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Algebraic Methods in Physics by Yvan Saint-Aubin,Luc Vinet Pdf

This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.

Author : Jürgen Fuchs
Publisher : Cambridge University Press
Page : 452 pages
File Size : 49,5 Mb
Release : 1995-03-09
Category : Mathematics
ISBN : 052148412X

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Affine Lie Algebras and Quantum Groups by Jürgen Fuchs Pdf

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Author : Naihuan Jing,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 42,9 Mb
Release : 1999
Category : Affine algebraic groups
ISBN : 9780821811993

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Recent Developments in Quantum Affine Algebras and Related Topics by Naihuan Jing,Kailash C. Misra Pdf

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

Author : Jürgen Fuchs,Christoph Schweigert
Publisher : Cambridge University Press
Page : 464 pages
File Size : 48,6 Mb
Release : 2003-10-07
Category : Mathematics
ISBN : 0521541190

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Symmetries, Lie Algebras and Representations by Jürgen Fuchs,Christoph Schweigert Pdf

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Author : André Gil Henriques,David Penneys,James E. Tener
Publisher : American Mathematical Society
Page : 100 pages
File Size : 48,5 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470455408

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Planar Algebras in Braided Tensor Categories by André Gil Henriques,David Penneys,James E. Tener Pdf

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Author : Philippe Francesco,Pierre Mathieu,David Senechal
Publisher : Springer Science & Business Media
Page : 908 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461222569

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Conformal Field Theory by Philippe Francesco,Pierre Mathieu,David Senechal Pdf

Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Author : Alan L. Carey,Michael K. Murray
Publisher : Cambridge University Press
Page : 308 pages
File Size : 47,9 Mb
Release : 1998
Category : Mathematics
ISBN : 0521624908

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Geometric Analysis and Lie Theory in Mathematics and Physics by Alan L. Carey,Michael K. Murray Pdf

Graduate lectures on the interface between mathematics and physics.

Author : Terry Gannon
Publisher : Cambridge University Press
Page : 493 pages
File Size : 48,9 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009401586

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Moonshine beyond the Monster by Terry Gannon Pdf

Author : Pierre Ramond
Publisher : Cambridge University Press
Page : 128 pages
File Size : 55,5 Mb
Release : 2010-05-13
Category : Science
ISBN : 9781139489645

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Group Theory by Pierre Ramond Pdf

Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac–Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.

Author : Peter West
Publisher : Cambridge University Press
Page : 723 pages
File Size : 46,5 Mb
Release : 2012-07-05
Category : Science
ISBN : 9781107393875

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Introduction to Strings and Branes by Peter West Pdf

Supersymmetry, strings and branes are believed to be the essential ingredients in a single unified consistent theory of physics. This book gives a detailed, step-by-step introduction to the theoretical foundations required for research in strings and branes. After a study of the different formulations of the bosonic and supersymmetric point particles, the classical and quantum bosonic and supersymmetric string theories are presented. This book includes accounts of brane dynamics and D-branes and the T, S and U duality symmetries of string theory. The historical derivation of string theory is given as well as the sum over the world-sheet approach to the interacting string. More advanced topics include string field theory and Kac–Moody symmetries. The book contains pedagogical accounts of conformal quantum field theory, supergravity theories, Clifford algebras and spinors, and Lie algebras. It is essential reading for graduate students and researchers wanting to learn strings and branes.

Author : Jiri Patera,Pavel Winternitz,Yvan Saint-Aubin,Luc Vinet
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 42,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0387951253

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Algebraic Methods in Physics by Jiri Patera,Pavel Winternitz,Yvan Saint-Aubin,Luc Vinet Pdf

Self-Similarities and Invariant Densities for Model Sets.- Model Sets and Self-Similarities.- Averaging Operators and Invariant Densities.- Further Remarks.- Outlook.- References.- Symmetry Operations in the Brain: Music and Reasoning.- Trion Model.- Music Enhances Spatial-Temporal Reasoning.- References.- Lie Modules of Bounded Multiplicities.- Simple L Modules with Finite-Dimensional Weight Spaces.- Completely Pointed Modules.- Completely Pointed Modules Tensored with Finite-Dimensional Modules.- References.- Moving Frames and Coframes.- References.- The Fibonacci-Deformed Harmonic Oscillator.- About Strictly Increasing Sequences of Positive Numbers.- Quantum Algebra Associated with the Spectrum ? = xn.- The ?-Natural Spectrum.- The Fibonacci Deformation of Weyl Algebra.- Coherent States and Some Special Functions.- References.- Continuous and Discrete Linearizable Systems: The Riccati Saga.- Brief Review of the Continuous Gambier Equation.- Discrete Analog of the Gambier Equation, Revisited.- Discrete Projective and Matrix Riccati Equations.- Discrete Conformai Riccati Equations.- Conclusions and Outlook.- References.- Superintegrability on Two-Dimensional Complex Euclidean Space.- Potential V5.- Potential V6.- Potential V7.- References.- Hydrodynamic Systems and the Higher-Dimensional Laplace Transformations of Cartan Submanifolds.- Hydrodynamic Systems Rich in Conservation Laws.- Applications of the Higher-Dimensional Laplace Transformation to Hydrodynamic Systems that are Rich in Conservation Laws.- References.- Branching Rules and Weight Multiplicities for Simple and Affine Lie Algebras.- Simple and Affine Lie Algebras.- Branching Rules for Simple Lie Algebras.- Young Diagrams and Branching Rules.- Weight Multiplicities of Simple Lie Algebras.- Young Tableaux and Weight Multiplicities.- Branching Rule Multiplicities for the Restriction from Affine to Simple Lie Algebras.- Branching Rules Derived from Characters.- Weight Multiplicities of Affine Lie Algebras.- References.- Conditions for the Existence of Higher Symmetries and Nonlinear Evolutionary Equations on the Lattice.- Construction of the Classifying Conditions.- The Toda Lattice Class.- References.- Complete Description of the Voronoï Cell of the Lie Algebra An Weight Lattice. On the Bounds for the Number of d-Faces of the n-Dimensional Voronoï Cells.- The Expression of the Bounds Nd(n) Obtained by Voronoï.- Detailed Description of the Voronoï Cells of the A(TM) Lattices.- The New Explicit Expression of Bounds Nd(n).- Expression of Nd(n) as Multiple of a Stirling Number of Second Kind.- Final Remarks.- References.- The Relativistic Oscillator and the Mass Spectra of Baryons.- The System of Three Relativistic Scalar Particles with Oscillator Interactions.- An Approach to the Spinorial Relativistic Three-Body System.- References.- Seiberg-Witten Theory Without Tears.- N = 2 Supersymmetry.- N = 2 Superaction.- Textbook Properties.- Spontaneous Symmetry-Breaking.- Holomorphy and Duality.- Perturbative and Nonperturbative F (A).- Preliminaries.- Fuchsian Maps.- The Schwarzian Derivatives.- SW Choice.- Correctness.- Uniqueness.- References.- Bargmann Representation for Some Deformed Harmonic Oscillators with Non-Fock Representation.- Representations.- Toward a Bargmann Representation.- The "q-Oscillator".- Generalization of the Previous Example.- Deformed Algebra Associated to a Given Weight function.- Bargmann Representations Corresponding to Different ?.- The Case of an Annulus.- Conclusion.- References.- The Vector-Coherent-State Inducing Construction for Clebsch-Gordan Coefficients.- Induced Representations of su(4).- SU(4) Clebsch-Gordan Coefficients.- Summary.- References.- Highest-Weight Representations of Borcherds Algebras.- Borcherds Algebras.- Cartan Subalgebra of an Affine Kac-Moody Algebra.- Adding Energy and Number Operators to the Cartan Subalgebra.- Conclusions.- References.- Graded Contractions of Lie Algebras of Physical Interest.- Notion of Graded

Author : Yavuz Nutku,Cihan Saclioglu,Teoman Turgut
Publisher : CRC Press
Page : 413 pages
File Size : 47,6 Mb
Release : 2018-03-14
Category : Science
ISBN : 9780429971426

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Conformal Field Theory by Yavuz Nutku,Cihan Saclioglu,Teoman Turgut Pdf

This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.