Representation Theory and Complex Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory and Complex Geometry write by Neil Chriss. This book was released on 1997. Representation Theory and Complex Geometry available in PDF, EPUB and Kindle. This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.
Representation Theory and Complex Geometry
Representation Theory and Complex Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory and Complex Geometry write by Neil Chriss. This book was released on 2009-12-24. Representation Theory and Complex Geometry available in PDF, EPUB and Kindle. "The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. Both are enlivened by examples related to groups...An attractive feature is the attempt to convey some informal ‘wisdom’ rather than only the precise definitions. As a number of results [are] due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory...it has already proved successful in introducing a new generation to the subject." (Bulletin of the AMS)
Hodge Theory, Complex Geometry, and Representation Theory
Hodge Theory, Complex Geometry, and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hodge Theory, Complex Geometry, and Representation Theory write by Mark Green. This book was released on 2013-11-05. Hodge Theory, Complex Geometry, and Representation Theory available in PDF, EPUB and Kindle. This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.
Representation Theory and Complex Analysis
Representation Theory and Complex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory and Complex Analysis write by Michael Cowling. This book was released on 2008-02-22. Representation Theory and Complex Analysis available in PDF, EPUB and Kindle. Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Representation Theory and Complex Geometry
Representation Theory and Complex Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory and Complex Geometry write by Victor Ginzburg. This book was released on 2005-05-01. Representation Theory and Complex Geometry available in PDF, EPUB and Kindle. [see attached] This second edition of {\it Representation Theory and Complex Geometry} provides an overview of significant advances in representation theory from a geometric standpoint. A geometrically-oriented treatment has long been desired, especially since the discovery of {\cal D}-modules in the early '80s and the quiver approach to quantum groups in the early '90s. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. Thus, Chapters 1-3 and 5-6 provide some basics in symplectic geometry, Borel--Moore homology, the geometry of semisimple groups, equivariant algebraic K-theory "from scratch," and the topology and algebraic geometry of flag varieties and conjugacy classes, respectively. The material covered by Chapters 5 and 6, as well as most of Chapter 3, has never been presented in book form. Chapters 3-4 and 7-8 present a uniform approach to representation theory of three quite different objects: Weyl groups, Lie algebra sln, and the Iwahori--Hecke algebra. The results of Chapters 4 and 8, with complete proofs are not to be found elsewhere in the literature. This second edition contains substantial updates and revisions to include more standard classical results in chapters 2, 3, 5, and 6 as well as two new chapters. Chapter 9 treats the applications of {\cal D}-modules to Lie groups, and includes the study of * Differential operators on a semisimple group and on its flag manifold; * the famous Beilinson--Bernstein Localization Theorem reducing the study of {\it g}-modules to that of {\cal D} modules; * the so-called Harish--Chandra holonomic system. Chapter 10 isdevoted to some very exciting developments connecting the representations of quantum groups to the geometry of "quiver varieties," introduced by Lusztig and Nakajima. The subject is closely related to many other important topics such as the McKay correspondence, semismall resolutions and Hilbert schemes. Overall, this chapter puts the representation theory of Kac--Moody algebras and quantum groups in this broader context. The exposition is practically self-contained with each chapter potentially serving as a basis for a graduate course or seminar. An excellent glossary of notation, comprehensive bibliography and extensive index round out this new edition. The techniques developed here play an essential role in the development of the Langlands program and can be successfully applied to representation theory, quantum groups and quantum field theory, affine Lie algebras, algebraic geometry, and mathematical physics.
