Infinite Dimensional Aspects Of Representation Theory And Applications

Author : Stephen Berman
Publisher : American Mathematical Soc.
ISBN 13 : 082183701X
Total Pages : 168 pages
Book Rating : 4.16/5 ( download)

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Download or read book Infinite-Dimensional Aspects of Representation Theory and Applications written by Stephen Berman and published by American Mathematical Soc.. This book was released on 2005 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

Author : Raymond C. Fabec
Publisher : CRC Press
ISBN 13 : 1351990217
Total Pages : 309 pages
Book Rating : 4.19/5 ( download)

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Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by CRC Press. This book was released on 2018-10-03 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

Author : Augustin Banyaga
Publisher : World Scientific
ISBN 13 : 9814488143
Total Pages : 176 pages
Book Rating : 4.43/5 ( download)

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Download or read book Infinite Dimensional Lie Groups in Geometry and Representation Theory written by Augustin Banyaga and published by World Scientific. This book was released on 2002-07-12 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics. Contents:Inheritance Properties for Lipschitz-Metrizable Frölicher Groups (J Teichmann)Around the Exponential Mapping (T Robart)On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras (J A Leslie)The Lie Group of Fourier Integral Operators on Open Manifolds (R Schmid)On Some Properties of Leibniz Algebroids (A Wade)On the Geometry of Locally Conformal Symplectic Manifolds (A Banyaga)Some Properties of Locally Conformal Symplectic Manifolds (S Haller)Criticality of Unit Contact Vector Fields (P Rukimbira)Orbifold Homeomorphism and Diffeomorphism Groups (J E Borzellino & V Brunsden)A Note on Isotopies of Symplectic and Poisson Structures (A Banyaga & P Donato)Remarks on Actions on Compacta by Some Infinite-Dimensional Groups (V Pestov) Readership: Graduate students and researchers in mathematics and mathematical physics. Keywords:

Author : Raymond C. Fabec
Publisher : CRC Press
ISBN 13 : 1482285770
Total Pages : 448 pages
Book Rating : 4.72/5 ( download)

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Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by CRC Press. This book was released on 2018-10-03 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

Author : Boris Khesin
Publisher : Springer Science & Business Media
ISBN 13 : 3540772634
Total Pages : 304 pages
Book Rating : 4.37/5 ( download)

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Download or read book The Geometry of Infinite-Dimensional Groups written by Boris Khesin and published by Springer Science & Business Media. This book was released on 2008-09-28 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
ISBN 13 : 012804683X
Total Pages : 512 pages
Book Rating : 4.38/5 ( download)

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Download or read book Introduction to Finite and Infinite Dimensional Lie (Super)algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras

Author : Palle Jorgensen
Publisher : World Scientific
ISBN 13 : 9811225796
Total Pages : 253 pages
Book Rating : 4.96/5 ( download)

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Download or read book Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory written by Palle Jorgensen and published by World Scientific. This book was released on 2021-01-15 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Author :
Publisher :
ISBN 13 : 9780821891162
Total Pages : 120 pages
Book Rating : 4.62/5 ( download)

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Download or read book Infinite-dimensional Representations of 2-groups written by and published by . This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: A `2-group' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, 2-groups have representations on `2-vector spaces', which are categories analogous to vector spaces. Unfortunately, Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional 2-vector spaces called `measurable categories' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie 2-groups. Here we continue this work. We begin with a detailed study of measurable categories. Then we give a geometrical description of the measurable representations, intertwiners and 2-intertwiners for any skeletal measurable 2-group. We study tensor products and direct sums for representations, and various concepts of subrepresentation. We describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory. We study irreducible and indecomposable representations and intertwiners. We also study `irretractable' representations--another feature not seen in ordinary group representation theory. Finally, we argue that measurable categories equipped with some extra structure deserve to be considered `separable 2-Hilbert spaces', and compare this idea to a tentative definition of 2-Hilbert spaces as representation categories of commutative von Neumann algebras.

Author : Victor G Kac
Publisher : World Scientific
ISBN 13 : 981452221X
Total Pages : 252 pages
Book Rating : 4.12/5 ( download)

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Download or read book Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras written by Victor G Kac and published by World Scientific. This book was released on 2013-07-05 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac–Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra. The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras — such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations — simplify and clarify the constructions of the first edition of the book. This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory. Contents:Definition of Positive-Energy Representations of VirComplete Reducibility of the Oscillator Representations of VirLie Algebras of Infinite MatricesBoson–Fermion CorrespondenceSchur PolynomialsN-Soliton SolutionsThe Kac Determinant FormulaNonabelian Generalization of Virasoro Operators: The Sugawara ConstructionThe Weyl–Kac Character Formula and Jacobi–Riemann Theta FunctionsCompletion of the Proof of the Kac Determinant FormulaLambda–Bracket of Local Formal DistributionsCompletion of U, Restricted Representations and Quantum FieldsNon-Commutative Wick FormulaConformal WeightsDefinition of a Vertex AlgebraDefinition of a Representation of a Vertex Algebraand other lectures Readership: Mathematicians studying representation theory and theoretical physicists. Keywords:Highest Weight Representations;Virasoro Algebra;Heisenberg Algebra;Infinite-Dimensional Lie Algebras;Boson–Fermion Correspondence;Sugawara Construction;Kac Determinant Formula;Vertex Operators;The KP Hierarchy;N-Solitons;Hirota's Bilinear Equations;Vertex Algebras;Quantum Fields;Energy-Momentum Field;Lambda-Bracket;Normal Ordered Product;Conformal Weight;Twisted Representations;Zhu Algebra;Charged Free Fermions;Neutral Free Fermions;Borcherds Identity;Twisted RepresentationsKey Features:The first part of the lectures demonstrates four related constructions of highest weight representations of infinite-dimensional algebras: Heisenberg algebra, Lie algebra $gl_\infty$, affine Kac–Moody algebras and the Virasoro algebra. The constructions originate from theoretical physics and are explained in full detailThe complete proof of the Kac determinant formula is providedThe second part of the lectures demonstrates how the notions of the theory of vertex algebras clarify and simplify the constructions of the first partThe introductory exposition is self-containedMany examples providedCan be used for graduate courses

Author : Caroline Gruson
Publisher : Springer
ISBN 13 : 3319982710
Total Pages : 223 pages
Book Rating : 4.17/5 ( download)

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Download or read book A Journey Through Representation Theory written by Caroline Gruson and published by Springer. This book was released on 2018-10-23 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.