Lie Theory And Geometry
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Lie Theory
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Author : Jean-Philippe Anker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lie Theory written by Jean-Philippe Anker 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.
* 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.
Lie Theory And Geometry
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Author : Jean-Luc Brylinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lie Theory And Geometry written by Jean-Luc Brylinski 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.
This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant’s fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant’s work.
Lie Groups Geometry And Representation Theory
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Author : Victor G. Kac
language : en
Publisher: Springer
Release Date : 2018-12-12
Lie Groups Geometry And Representation Theory written by Victor G. Kac and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.
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)
New Developments In Lie Theory And Geometry
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Author : Carolyn Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
New Developments In Lie Theory And Geometry written by Carolyn Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Geometry, Differential categories.
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.
Developments And Retrospectives In Lie Theory
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Author : Geoffrey Mason
language : en
Publisher: Springer
Release Date : 2014-11-12
Developments And Retrospectives In Lie Theory written by Geoffrey Mason and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-12 with Mathematics categories.
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.
Structure And Geometry Of Lie Groups
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Author : Joachim Hilgert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-06
Structure And Geometry Of Lie Groups written by Joachim Hilgert 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 2011-11-06 with Mathematics categories.
This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
Emergence Of The Theory Of Lie Groups
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Author : Thomas Hawkins
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Emergence Of The Theory Of Lie Groups written by Thomas Hawkins 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 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.
Lie Theory
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Author : Jean-Philippe Anker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-25
Lie Theory written by Jean-Philippe Anker 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 2006-02-25 with Mathematics categories.
* Presents extensive surveys by van den Ban, Schlichtkrull, and Delorme of the recent progress in deriving the Plancherel theorem on reductive symmetric spaces * Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology * Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required
Lie Groups And Lie Algebras I
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Author : V.V. Gorbatsevich
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-12-18
Lie Groups And Lie Algebras I written by V.V. Gorbatsevich 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 1996-12-18 with Mathematics categories.
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
Geometry Lie Theory And Applications
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Author : Sigbjørn Hervik
language : en
Publisher: Springer Nature
Release Date : 2022-02-07
Geometry Lie Theory And Applications written by Sigbjørn Hervik and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-07 with Mathematics categories.
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.