Dirac Operators In Representation Theory

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Dirac Operators in Representation Theory

Jing-Song Huang,Pavle Pandzic
Dirac Operators in Representation Theory Book PDF

Author : Jing-Song Huang,Pavle Pandzic
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 41,8 Mb
Release : 2007-05-27
Category : Mathematics
ISBN : 9780817644932

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Dirac Operators in Representation Theory by Jing-Song Huang,Pavle Pandzic Pdf

This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.

An Introduction to Dirac Operators on Manifolds

Jan Cnops
An Introduction to Dirac Operators on Manifolds Book PDF

Author : Jan Cnops
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200659

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An Introduction to Dirac Operators on Manifolds by Jan Cnops Pdf

The chapters on Clifford algebra and differential geometry can be used as an introduction to the topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.; The more advanced reader will appreciate the fresh approach to the theory, as well as the new results on boundary value theory.; Concise, but self-contained text at the introductory grad level. Systematic exposition.; Clusters well with other Birkhäuser titles in mathematical physics.; Appendix. General Manifolds * List of Symbols * Bibliography * Index

Heat Kernels and Dirac Operators

Nicole Berline,Ezra Getzler,Michèle Vergne
Heat Kernels and Dirac Operators Book PDF

Author : Nicole Berline,Ezra Getzler,Michèle Vergne
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 48,9 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540200622

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Heat Kernels and Dirac Operators by Nicole Berline,Ezra Getzler,Michèle Vergne Pdf

In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.

Clifford Algebras and Dirac Operators in Harmonic Analysis

John E. Gilbert,Margaret Anne Marie Murray
Clifford Algebras and Dirac Operators in Harmonic Analysis Book PDF

Author : John E. Gilbert,Margaret Anne Marie Murray
Publisher : Cambridge University Press
Page : 346 pages
File Size : 49,8 Mb
Release : 1991-07-26
Category : Mathematics
ISBN : 0521346541

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Clifford Algebras and Dirac Operators in Harmonic Analysis by John E. Gilbert,Margaret Anne Marie Murray Pdf

The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Operators and Representation Theory

Palle E.T. Jorgensen
Operators and Representation Theory Book PDF

Author : Palle E.T. Jorgensen
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 49,5 Mb
Release : 2017-05-22
Category : Science
ISBN : 9780486822570

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Operators and Representation Theory by Palle E.T. Jorgensen Pdf

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

Dirac Operators in Analysis

John Ryan,Daniele C Struppa
Dirac Operators in Analysis Book PDF

Author : John Ryan,Daniele C Struppa
Publisher : CRC Press
Page : 260 pages
File Size : 43,9 Mb
Release : 1999-01-06
Category : Mathematics
ISBN : 0582356814

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Dirac Operators in Analysis by John Ryan,Daniele C Struppa Pdf

Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.

Lie Groups, Geometry, and Representation Theory

Victor G. Kac,Vladimir L. Popov
Lie Groups Geometry and Representation Theory Book PDF

Author : Victor G. Kac,Vladimir L. Popov
Publisher : Springer
Page : 540 pages
File Size : 55,6 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9783030021917

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Lie Groups, Geometry, and Representation Theory by Victor G. Kac,Vladimir L. Popov Pdf

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)

Dirac Operators in Riemannian Geometry

Thomas Friedrich
Dirac Operators in Riemannian Geometry Book PDF

Author : Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 213 pages
File Size : 51,7 Mb
Release : 2000
Category : Dirac equation
ISBN : 9780821820551

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Dirac Operators in Riemannian Geometry by Thomas Friedrich Pdf

For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants. In this text, Friedrich examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and $\textrm{spin}mathbb{C}$ structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections. This detailed book with elegant proofs is suitable as a text for courses in advanced differential geometry and global analysis, and can serve as an introduction for further study in these areas. This edition is translated from the German edition published by Vieweg Verlag.

Dirac Operators and Spectral Geometry

Giampiero Esposito
Dirac Operators and Spectral Geometry Book PDF

Author : Giampiero Esposito
Publisher : Cambridge University Press
Page : 227 pages
File Size : 53,7 Mb
Release : 1998-08-20
Category : Mathematics
ISBN : 9780521648622

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Dirac Operators and Spectral Geometry by Giampiero Esposito Pdf

A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.

Perspectives in Lie Theory

Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Perspectives in Lie Theory Book PDF

Author : Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Publisher : Springer
Page : 461 pages
File Size : 53,5 Mb
Release : 2017-12-07
Category : Mathematics
ISBN : 9783319589718

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Perspectives in Lie Theory by Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole Pdf

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Lie Theory and Its Applications in Physics

Vladimir Dobrev
Lie Theory and Its Applications in Physics Book PDF

Author : Vladimir Dobrev
Publisher : Springer
Page : 614 pages
File Size : 55,7 Mb
Release : 2016-12-10
Category : Science
ISBN : 9789811026362

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

A Spinorial Approach to Riemannian and Conformal Geometry

Anonim
A Spinorial Approach to Riemannian and Conformal Geometry Book PDF

Author : Anonim
Publisher : Unknown
Page : 452 pages
File Size : 53,5 Mb
Release : 2015
Category : MATHEMATICS
ISBN : 303719636X

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A Spinorial Approach to Riemannian and Conformal Geometry by Anonim Pdf

The book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator which plays a fundamental role in differential geometry and mathematical physics. After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces. The special features of the book include a unified treatment of Spin$^\mathrm c$ and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors. This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry.

Introduction to Symplectic Dirac Operators

Katharina Habermann,Lutz Habermann
Introduction to Symplectic Dirac Operators Book PDF

Author : Katharina Habermann,Lutz Habermann
Publisher : Springer
Page : 131 pages
File Size : 54,7 Mb
Release : 2006-10-28
Category : Mathematics
ISBN : 9783540334217

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Introduction to Symplectic Dirac Operators by Katharina Habermann,Lutz Habermann Pdf

This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.

Affine, Vertex and W-algebras

Dražen Adamović,Paolo Papi
Affine Vertex and W algebras Book PDF

Author : Dražen Adamović,Paolo Papi
Publisher : Springer Nature
Page : 218 pages
File Size : 48,7 Mb
Release : 2019-11-28
Category : Mathematics
ISBN : 9783030329068

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Affine, Vertex and W-algebras by Dražen Adamović,Paolo Papi Pdf

This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.

Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology

David E. Evans,Masamichi Takesaki
Operator Algebras and Applications Volume 1 Structure Theory K theory Geometry and Topology Book PDF

Author : David E. Evans,Masamichi Takesaki
Publisher : Cambridge University Press
Page : 257 pages
File Size : 49,5 Mb
Release : 1988
Category : Mathematics
ISBN : 9780521368438

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Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology by David E. Evans,Masamichi Takesaki Pdf

These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.