Operators And Representation Theory
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Operators And Representation Theory
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Author : Palle E.T. Jorgensen
language : en
Publisher: Courier Dover Publications
Release Date : 2017-05-22
Operators And Representation Theory written by Palle E.T. Jorgensen and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-22 with Science categories.
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.
Operators And Representation Theory
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Author : P.E.T. Jorgensen
language : en
Publisher: North Holland
Release Date : 1988
Operators And Representation Theory written by P.E.T. Jorgensen and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra.Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem.Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers.
Unbounded Operator Algebras And Representation Theory
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Author : K. Schmüdgen
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Unbounded Operator Algebras And Representation Theory written by K. Schmüdgen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
*-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.
Dirac Operators In Representation Theory
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Author : Jing-Song Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-27
Dirac Operators In Representation Theory written by Jing-Song Huang 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 2007-05-27 with Mathematics categories.
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.
Theory Of Group Representations And Applications
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Author : Asim Orhan Barut
language : en
Publisher: World Scientific
Release Date : 1986
Theory Of Group Representations And Applications written by Asim Orhan Barut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Elements Of The Representation Theory Of The Jacobi Group
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Author : Rolf Berndt
language : en
Publisher: Birkhäuser
Release Date : 2013-11-09
Elements Of The Representation Theory Of The Jacobi Group written by Rolf Berndt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.
Algebraic Methods In Operator Theory
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Author : Raul E. Curto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Methods In Operator Theory written by Raul E. Curto 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.
The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify ing theme is the algebraic view and approach to the study of operators and their applications. The complementarity between the diversity of topics on the one hand and the unity of ideas on the other has been stressed. Some of the longer contributions represent material from lectures (in expanded form and with proofs for the most part). However, the shorter papers, as well as the longer ones, are an integral part of the picture; they have all been carefully refereed and revised with a view to a unity of purpose, timeliness, readability, and broad appeal. Raul Curto and Paile E. T.
Lectures On Representation Theory
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Author : Jing-Song Huang
language : en
Publisher: World Scientific
Release Date : 1999
Lectures On Representation Theory written by Jing-Song Huang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.
Unbounded Operator Algebras And Representation Theory
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Author : Konrad Schmüdgen
language : en
Publisher:
Release Date : 1990
Unbounded Operator Algebras And Representation Theory written by Konrad Schmüdgen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Operator algebras categories.
Lectures On Gaussian Integral Operators And Classical Groups
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Author : Yu. A. Neretin
language : en
Publisher: European Mathematical Society
Release Date : 2011
Lectures On Gaussian Integral Operators And Classical Groups written by Yu. A. Neretin and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometry, Differential categories.
This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis.