New Developments In Lie Theory And Geometry

Author : Carolyn Gordon
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 48,6 Mb
Release : 2009
Category : Geometry, Differential
ISBN : 9780821846513

Get Book

New Developments in Lie Theory and Geometry by Carolyn Gordon Pdf

This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.

Author : Geoffrey Mason,Ivan Penkov,Joseph A. Wolf
Publisher : Springer
Page : 268 pages
File Size : 51,9 Mb
Release : 2014-11-12
Category : Mathematics
ISBN : 9783319099347

Get Book

Developments and Retrospectives in Lie Theory by Geoffrey Mason,Ivan Penkov,Joseph A. Wolf Pdf

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. At the beginning, the top universities in California and Utah hosted the meetings, which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. These Lie theory workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. The contributors have all participated in these Lie theory workshops and include in this volume expository articles which will cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Author : Juan Tirao,Wallach
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461229780

Get Book

New Developments in Lie Theory and Their Applications by Juan Tirao,Wallach Pdf

Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In August-September 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented.

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 54,5 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

Get Book

Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Author : Geoffrey Mason,Ivan Penkov,Joseph A. Wolf
Publisher : Unknown
Page : 408 pages
File Size : 46,7 Mb
Release : 2014-11-30
Category : Electronic
ISBN : 3319098055

Get Book

Developments and Retrospectives in Lie Theory by Geoffrey Mason,Ivan Penkov,Joseph A. Wolf Pdf

Author : V.V. Gorbatsevich,E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 552 pages
File Size : 44,7 Mb
Release : 1996-12-18
Category : Mathematics
ISBN : 354061222X

Get Book

Lie Groups and Lie Algebras I by V.V. Gorbatsevich,E.B. Vinberg Pdf

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Author : Victor G. Kac,Vladimir L. Popov
Publisher : Springer
Page : 540 pages
File Size : 43,6 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9783030021917

Get Book

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)

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681920

Get Book

Lie Theory by Jean-Philippe Anker,Bent Orsted Pdf

* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Author : Mark R. Sepanski
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 47,5 Mb
Release : 2007-04-05
Category : Mathematics
ISBN : 9780387491585

Get Book

Compact Lie Groups by Mark R. Sepanski Pdf

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Coverage includes the construction of the Spin groups, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel-Weil Theorem. The book develops the necessary Lie algebra theory with a streamlined approach focusing on linear Lie groups.

Author : Vladimir Dobrev
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 40,8 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9784431542704

Get Book

Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation 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. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics” held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.

Author : Vladimir Dobrev
Publisher : Springer
Page : 614 pages
File Size : 53,9 Mb
Release : 2016-12-10
Category : Science
ISBN : 9789811026362

Get Book

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.

Author : Tao Qian,Thomas Hempfling,Alan McIntosh,Franciscus Sommen
Publisher : Birkhäuser
Page : 380 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878388

Get Book

Advances in Analysis and Geometry by Tao Qian,Thomas Hempfling,Alan McIntosh,Franciscus Sommen Pdf

At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. This book collects refereed papers from a satellite conference to the ICM 2002, plus invited contributions. All articles contain unpublished new results.

Author : V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Publisher : Springer
Page : 238 pages
File Size : 40,7 Mb
Release : 2011-12-24
Category : Mathematics
ISBN : 3642580009

Get Book

Lie Groups and Lie Algebras I by V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg Pdf

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Author : Sigbjørn Hervik,Boris Kruglikov,Irina Markina,Dennis The
Publisher : Springer Nature
Page : 337 pages
File Size : 51,5 Mb
Release : 2022-02-07
Category : Mathematics
ISBN : 9783030812966

Get Book

Geometry, Lie Theory and Applications by Sigbjørn Hervik,Boris Kruglikov,Irina Markina,Dennis The Pdf

This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.

Author : Thomas Hawkins
Publisher : Springer Science & Business Media
Page : 578 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212027

Get Book

Emergence of the Theory of Lie Groups by Thomas Hawkins Pdf

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.