Unitary Representations Of Reductive Lie Groups

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Unitary Representations of Reductive Lie Groups

Author : David A. Vogan
Publisher : Princeton University Press
ISBN 13 : 9780691084824
Total Pages : 324 pages
Book Rating : 4.0/5 (848 download)

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Book Synopsis Unitary Representations of Reductive Lie Groups by : David A. Vogan

Download or read book Unitary Representations of Reductive Lie Groups written by David A. Vogan and published by Princeton University Press. This book was released on 1987-10-21 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.

Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118

Author : David A. Vogan Jr.
Publisher : Princeton University Press
ISBN 13 : 1400882389
Total Pages : 320 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 by : David A. Vogan Jr.

Download or read book Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 written by David A. Vogan Jr. and published by Princeton University Press. This book was released on 2016-03-02 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.

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.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Algebraic and Analytic Methods in Representation Theory

Author :
Publisher : Elsevier
ISBN 13 : 0080526950
Total Pages : 357 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Algebraic and Analytic Methods in Representation Theory by :

Download or read book Algebraic and Analytic Methods in Representation Theory written by and published by Elsevier. This book was released on 1996-09-27 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field

Lie Groups, Lie Algebras, and Representations

Author : Brian C. Hall
Publisher : Springer Science & Business Media
ISBN 13 : 9780387401225
Total Pages : 376 pages
Book Rating : 4.4/5 (12 download)

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Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian C. Hall

Download or read book Lie Groups, Lie Algebras, and Representations written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2003-08-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.

Lie Theory

Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
ISBN 13 : 0817681922
Total Pages : 341 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Lie Theory by : Jean-Philippe Anker

Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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.

Unitary Representations of Real Reductive Groups

Author : Jeffrey Adams
Publisher :
ISBN 13 : 9782856299180
Total Pages : 174 pages
Book Rating : 4.2/5 (991 download)

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Book Synopsis Unitary Representations of Real Reductive Groups by : Jeffrey Adams

Download or read book Unitary Representations of Real Reductive Groups written by Jeffrey Adams and published by . This book was released on 2020 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Algebras and Lie Groups

Author : Jean-Pierre Serre
Publisher : Springer
ISBN 13 : 3540706348
Total Pages : 180 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Lie Algebras and Lie Groups by : Jean-Pierre Serre

Download or read book Lie Algebras and Lie Groups written by Jean-Pierre Serre and published by Springer. This book was released on 2009-02-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups

Author : Armand Borel
Publisher : American Mathematical Soc.
ISBN 13 : 147041225X
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups by : Armand Borel

Download or read book Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2013-11-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.

Representations of Finite Groups of Lie Type

Author : François Digne
Publisher : Cambridge University Press
ISBN 13 : 1108481485
Total Pages : 267 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Representations of Finite Groups of Lie Type by : François Digne

Download or read book Representations of Finite Groups of Lie Type written by François Digne and published by Cambridge University Press. This book was released on 2020-03-05 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.

The Langlands Classification and Irreducible Characters for Real Reductive Groups

Author : J. Adams
Publisher : Springer Science & Business Media
ISBN 13 : 146120383X
Total Pages : 331 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Langlands Classification and Irreducible Characters for Real Reductive Groups by : J. Adams

Download or read book The Langlands Classification and Irreducible Characters for Real Reductive Groups written by J. Adams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.

Representation Theory of Lie Groups

Author : M. F. Atiyah
Publisher : Cambridge University Press
ISBN 13 : 0521226368
Total Pages : 349 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Representation Theory of Lie Groups by : M. F. Atiyah

Download or read book Representation Theory of Lie Groups written by M. F. Atiyah and published by Cambridge University Press. This book was released on 1979 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.

Representations of Compact Lie Groups

Author : T. Bröcker
Publisher : Springer Science & Business Media
ISBN 13 : 3662129183
Total Pages : 323 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Representations of Compact Lie Groups by : T. Bröcker

Download or read book Representations of Compact Lie Groups written by T. Bröcker and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.

Representations of Algebraic Groups

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
ISBN 13 : 082184377X
Total Pages : 594 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representations of Algebraic Groups by : Jens Carsten Jantzen

Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Lie Groups, Lie Algebras, and Representations

Author : Brian Hall
Publisher : Springer
ISBN 13 : 3319134671
Total Pages : 452 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian Hall

Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette

Representation Theories and Algebraic Geometry

Author : A. Broer
Publisher : Springer Science & Business Media
ISBN 13 : 9401591318
Total Pages : 455 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Representation Theories and Algebraic Geometry by : A. Broer

Download or read book Representation Theories and Algebraic Geometry written by A. Broer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.