The Penrose Transform And Analytic Cohomology In Representation Theory

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The Penrose Transform and Analytic Cohomology in Representation Theory

Author : Michael G. Eastwood
Publisher : American Mathematical Soc.
ISBN 13 : 0821851764
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Penrose Transform and Analytic Cohomology in Representation Theory by : Michael G. Eastwood

Download or read book The Penrose Transform and Analytic Cohomology in Representation Theory written by Michael G. Eastwood and published by American Mathematical Soc.. This book was released on 1993 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains refereed papers presented at the AMS-IMS-SIAM Summer Research Conference on the Penrose Transform and Analytic Cohomology in Representation Theory held in the summer of 1992 at Mount Holyoke College. The conference brought together some of the top experts in representation theory and differential geometry. One of the issues explored at the conference was the fact that various integral transforms from representation theory, complex integral geometry, and mathematical physics appear to be instances of the same general construction, which is sometimes called the ``Penrose transform''. There is considerable scope for further research in this area, and this book would serve as an excellent introduction.

The Penrose Transform

Author : Robert J. Baston
Publisher : Courier Dover Publications
ISBN 13 : 0486797295
Total Pages : 257 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis The Penrose Transform by : Robert J. Baston

Download or read book The Penrose Transform written by Robert J. Baston and published by Courier Dover Publications. This book was released on 2016-11-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Brings to the reader a huge amount of information, well organized and condensed into less than two hundred pages." — Mathematical Reviews In recent decades twistor theory has become an important focus for students of mathematical physics. Central to twistor theory is the geometrical transform known as the Penrose transform, named for its groundbreaking developer. Geared toward students of physics and mathematics, this advanced text explores the Penrose transform and presupposes no background in twistor theory and a minimal familiarity with representation theory. An introductory chapter sketches the development of the Penrose transform, followed by reviews of Lie algebras and flag manifolds, representation theory and homogeneous vector bundles, and the Weyl group and the Bott-Borel-Weil theorem. Succeeding chapters explore the Penrose transform in terms of the Bernstein-Gelfand-Gelfand resolution, followed by worked examples, constructions of unitary representations, and module structures on cohomology. The treatment concludes with a review of constructions and suggests further avenues for research.

Representation Theory of Lie Groups

Author : Jeffrey Adams
Publisher : American Mathematical Soc.
ISBN 13 : 1470423146
Total Pages : 340 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representation Theory of Lie Groups by : Jeffrey Adams

Download or read book Representation Theory of Lie Groups written by Jeffrey Adams and published by American Mathematical Soc.. This book was released on 2015-06-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification. Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant "philosophy of coadjoint orbits" for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of "localization". And Jian-Shu Li covers Howe's theory of "dual reductive pairs". Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Representation Theory, Complex Analysis, and Integral Geometry

Author : Bernhard Krötz
Publisher : Springer Science & Business Media
ISBN 13 : 081764816X
Total Pages : 282 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Representation Theory, Complex Analysis, and Integral Geometry by : Bernhard Krötz

Download or read book Representation Theory, Complex Analysis, and Integral Geometry written by Bernhard Krötz and published by Springer Science & Business Media. This book was released on 2011-12-13 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.

Representation Theory and Harmonic Analysis

Author : Ray Alden Kunze
Publisher : American Mathematical Soc.
ISBN 13 : 0821803107
Total Pages : 270 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory and Harmonic Analysis by : Ray Alden Kunze

Download or read book Representation Theory and Harmonic Analysis written by Ray Alden Kunze and published by American Mathematical Soc.. This book was released on 1995 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume stems from a special session on representation theory and harmonic analysis held in honour of Ray Kunze at the 889th meeting of the American Mathematical Society on January 12-15 1994. It is intended for graduate students and research mathematicians interested in topological groups, lie groups and abstract harmonic analysis.

Representation Theory and Analysis on Homogeneous Spaces

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
ISBN 13 : 082180300X
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory and Analysis on Homogeneous Spaces by : Semen Grigorʹevich Gindikin

Download or read book Representation Theory and Analysis on Homogeneous Spaces written by Semen Grigorʹevich Gindikin and published by American Mathematical Soc.. This book was released on 1994 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A combination of new results and surveys of recent work on representation theory and the harmonic analysis of real and p-adic groups. Among the topics are nilpotent homogeneous spaces, multiplicity formulas for induced representations, and new methods for constructing unitary representations of real reductive groups. The 12 papers are from a conference at Rutgers University, February 1993. No index. Annotation copyright by Book News, Inc., Portland, OR

Transformation Groups and Representation Theory

Author : T. Tom Dieck
Publisher : Springer
ISBN 13 : 3540385177
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Transformation Groups and Representation Theory by : T. Tom Dieck

Download or read book Transformation Groups and Representation Theory written by T. Tom Dieck and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hodge Theory, Complex Geometry, and Representation Theory

Author : Mark Green
Publisher : American Mathematical Soc.
ISBN 13 : 1470410125
Total Pages : 314 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hodge Theory, Complex Geometry, and Representation Theory by : Mark Green

Download or read book Hodge Theory, Complex Geometry, and Representation Theory written by Mark Green and published by American Mathematical Soc.. This book was released on 2013-11-05 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representations of Reductive Groups

Author : Monica Nevins
Publisher : Birkhäuser
ISBN 13 : 3319234439
Total Pages : 532 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Representations of Reductive Groups by : Monica Nevins

Download or read book Representations of Reductive Groups written by Monica Nevins and published by Birkhäuser. This book was released on 2015-12-18 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Cohomological Induction and Unitary Representations (PMS-45), Volume 45

Author : Anthony W. Knapp
Publisher : Princeton University Press
ISBN 13 : 1400883938
Total Pages : 968 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Cohomological Induction and Unitary Representations (PMS-45), Volume 45 by : Anthony W. Knapp

Download or read book Cohomological Induction and Unitary Representations (PMS-45), Volume 45 written by Anthony W. Knapp and published by Princeton University Press. This book was released on 2016-06-02 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.

Lie Algebras, Cohomology, and New Applications to Quantum Mechanics

Author : Niky Kamran
Publisher : American Mathematical Soc.
ISBN 13 : 0821851691
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Algebras, Cohomology, and New Applications to Quantum Mechanics by : Niky Kamran

Download or read book Lie Algebras, Cohomology, and New Applications to Quantum Mechanics written by Niky Kamran and published by American Mathematical Soc.. This book was released on 1994 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

Invitations to Geometry and Topology

Author : Martin R. Bridson
Publisher :
ISBN 13 : 9780198507727
Total Pages : 352 pages
Book Rating : 4.5/5 (77 download)

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Book Synopsis Invitations to Geometry and Topology by : Martin R. Bridson

Download or read book Invitations to Geometry and Topology written by Martin R. Bridson and published by . This book was released on 2002 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation.

Radon Transforms and Tomography

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 0821821350
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Radon Transforms and Tomography by : Eric Todd Quinto

Download or read book Radon Transforms and Tomography written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2001 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

Special Values of Automorphic Cohomology Classes

Author : Mark Green
Publisher : American Mathematical Soc.
ISBN 13 : 0821898574
Total Pages : 145 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Special Values of Automorphic Cohomology Classes by : Mark Green

Download or read book Special Values of Automorphic Cohomology Classes written by Mark Green and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.

Topology and Representation Theory

Author : Eric M. Friedlander
Publisher : American Mathematical Soc.
ISBN 13 : 0821851659
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topology and Representation Theory by : Eric M. Friedlander

Download or read book Topology and Representation Theory written by Eric M. Friedlander and published by American Mathematical Soc.. This book was released on 1994 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: During 1991-1992, Northwestern University conducted a special emphasis year on the topic, "The connections between topology and representation theory." Activities over the year culminated in a conference in May 1992 which attracted over 120 participants. Most of the plenary lectures at the conference were expository and designed to introduce current trends to graduate students and nonspecialists familiar with algebraic topology. This volume contains refereed papers presented or solicited at the conference; one paper is based on a seminar given during the emphasis year.

Analysis and Geometry in Several Complex Variables

Author : Gen Komatsu
Publisher : Springer Science & Business Media
ISBN 13 : 1461221668
Total Pages : 322 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Analysis and Geometry in Several Complex Variables by : Gen Komatsu

Download or read book Analysis and Geometry in Several Complex Variables written by Gen Komatsu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

Global Differential Geometry

Author : Alfred Gray
Publisher : American Mathematical Soc.
ISBN 13 : 0821827502
Total Pages : 490 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Global Differential Geometry by : Alfred Gray

Download or read book Global Differential Geometry written by Alfred Gray and published by American Mathematical Soc.. This book was released on 2001 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alfred Gray's work covered a great part of differential geometry. In September 2000, a remarkable International Congress on Differential Geometry was held in his memory in Bilbao, Spain. Mathematicians from all over the world, representing 24 countries, attended the event. This volume includes major contributions by well known mathematicians (T. Banchoff, S. Donaldson, H. Ferguson, M. Gromov, N. Hitchin, A. Huckleberry, O. Kowalski, V. Miquel, E. Musso, A. Ros, S. Salamon, L. Vanhecke, P. Wellin and J.A. Wolf), the interesting discussion from the round table moderated by J.-P. Bourguignon, and a carefully selected and refereed selection of the Short Communications presented at the Congress. This book represents the state of the art in modern differential geometry, with some general expositions of some of the more active areas: special Riemannian manifolds, Lie groups and homogeneous spaces, complex structures, symplectic manifolds, geometry of geodesic spheres and tubes and related problems, geometry of surfaces, and computer graphics in differential geometry.