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• catalog abstract ""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.". "Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researcher. 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."--BOOK JACKET.".
• catalog contributor b11694161.
• catalog contributor b11694162.
• catalog created "c2000.".
• catalog date "2000".
• catalog date "c2000.".
• catalog dateCopyrighted "c2000.".
• catalog description ""Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researcher. 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."--BOOK JACKET.".
• catalog description ""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.".".
• catalog description "Includes bibliographical references.".
• catalog description "Representations of Semisimple Lie Groups / Anthony W. Knapp, Peter E. Trapa -- Motivation -- Some Representations of SL(n, R) -- Semisimple Groups and Structure Theory -- Introduction to Representation Theory -- Cartan Subalgebras and Highest Weights -- Action by the Lie Algebra -- Cartan Subgroups and Global Characters -- Discrete Series and Asymptotics -- Langlands Classifications -- Representations in Dolbeault Cohomology / Roger Zierau -- Complex Flag Varieties and Orbits Under a Real Form -- Open G[subscript 0]-Orbits -- Examples, Homogeneous Bundles -- Dolbeault Cohomology, Bott-Borel-Weil Theorem -- Indefinite Harmonic Theory -- Intertwining Operators I -- Intertwining Operators II -- The Linear Cycle Space -- Unitary Representations Attached to Elliptic Orbits. A Geometric Approach / Leticia Barchini -- Globalizations -- Dolbeault Cohomology and Maximal Globalization -- L[superscript 2]-Cohomology and Discrete Series Representations -- Indefinite Quantization -- The Method of Coadjoint Orbits for Real Reductive Groups / David A. Vogan, Jr. -- Some Ideas from Mathematical Physics -- The Jordan Decomposition and Three Kinds of Quantization -- Complex Polarizations -- The Kostant-Sekiguchi Correspondence -- Quantizing the Action of K -- Associated Graded Modules -- A Good Basis for Associated Graded Modules -- Proving Unitarity -- Geometric Methods in Representation Theory / Kari Vilonen -- Derived Categories of Constructible Sheaves -- Equivariant Derived Categories -- Functors to Representations -- Matsuki correspondence for sheaves -- Characteristic cycles -- The character formula -- Microlocalization of Matsuki = Sekiguchi -- Minimal representatons and reductive dual pairs -- The oscillator representation -- Models -- Duality -- Classification -- Unitarity -- Minimal representations of classical groups -- Dual pairs in simple groups.".
• catalog extent "xii, 340 p. ;".
• catalog identifier "0821819410 (alk. paper)".
• catalog isPartOf "IAS/Park City mathematics series ; v. 8".
• catalog issued "2000".
• catalog issued "c2000.".
• catalog language "eng".
• catalog publisher "Providence, R.I. : American Mathematical Society,".
• catalog subject "512/.55 21".
• catalog subject "Lie groups.".
• catalog subject "QA387 .R457 2000".
• catalog subject "Representations of Lie groups.".
• catalog subject "Representations of groups.".
• catalog tableOfContents "Representations of Semisimple Lie Groups / Anthony W. Knapp, Peter E. Trapa -- Motivation -- Some Representations of SL(n, R) -- Semisimple Groups and Structure Theory -- Introduction to Representation Theory -- Cartan Subalgebras and Highest Weights -- Action by the Lie Algebra -- Cartan Subgroups and Global Characters -- Discrete Series and Asymptotics -- Langlands Classifications -- Representations in Dolbeault Cohomology / Roger Zierau -- Complex Flag Varieties and Orbits Under a Real Form -- Open G[subscript 0]-Orbits -- Examples, Homogeneous Bundles -- Dolbeault Cohomology, Bott-Borel-Weil Theorem -- Indefinite Harmonic Theory -- Intertwining Operators I -- Intertwining Operators II -- The Linear Cycle Space -- Unitary Representations Attached to Elliptic Orbits. A Geometric Approach / Leticia Barchini -- Globalizations -- Dolbeault Cohomology and Maximal Globalization -- L[superscript 2]-Cohomology and Discrete Series Representations -- Indefinite Quantization -- The Method of Coadjoint Orbits for Real Reductive Groups / David A. Vogan, Jr. -- Some Ideas from Mathematical Physics -- The Jordan Decomposition and Three Kinds of Quantization -- Complex Polarizations -- The Kostant-Sekiguchi Correspondence -- Quantizing the Action of K -- Associated Graded Modules -- A Good Basis for Associated Graded Modules -- Proving Unitarity -- Geometric Methods in Representation Theory / Kari Vilonen -- Derived Categories of Constructible Sheaves -- Equivariant Derived Categories -- Functors to Representations -- Matsuki correspondence for sheaves -- Characteristic cycles -- The character formula -- Microlocalization of Matsuki = Sekiguchi -- Minimal representatons and reductive dual pairs -- The oscillator representation -- Models -- Duality -- Classification -- Unitarity -- Minimal representations of classical groups -- Dual pairs in simple groups.".
• catalog title "Representation theory of Lie groups / Jeffrey Adams, David Vogan, editors.".
• catalog type "text".