The Bala Carter Classification Of Nilpotent Orbits Of Semisimple Lie Algebras
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The Bala Carter Classification Of Nilpotent Orbits Of Semisimple Lie Algebras
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Author : Andriamananjara Tantely Rakotoarisoa
language : en
Publisher:
Release Date : 2017
The Bala Carter Classification Of Nilpotent Orbits Of Semisimple Lie Algebras written by Andriamananjara Tantely Rakotoarisoa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Conjugacy classes of nilpotent elements in complex semisimple Lie algebras are classified using the Bala-Carter theory. In this theory, nilpotent orbits in g are parametrized by the conjugacy classes of pairs (l,pl) of Levi subalgebras of g and distinguished parabolic subalgebras of [l,l]. In this thesis we present this theory and use it to give a list of representatives for nilpotent orbits in so(8) and from there we give a partition-type parametrization of them.
Nilpotent Orbits In Semisimple Lie Algebra
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Author : William.M. McGovern
language : en
Publisher: Routledge
Release Date : 2017-10-19
Nilpotent Orbits In Semisimple Lie Algebra written by William.M. McGovern and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.
Nilpotent Orbits In Semisimple Lie Algebras
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Author : William M. McGovern
language : en
Publisher:
Release Date : 1993
Nilpotent Orbits In Semisimple Lie Algebras written by William M. McGovern and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with MATHEMATICS categories.
"Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington."--Provided by publisher.
Nilpotent Orbits In Semisimple Lie Algebra
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Author : David .H. Collingwood
language : en
Publisher: CRC Press
Release Date : 1993-04-01
Nilpotent Orbits In Semisimple Lie Algebra written by David .H. Collingwood and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-01 with Mathematics categories.
The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary.
Algebraic Quotients Torus Actions And Cohomology The Adjoint Representation And The Adjoint Action
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Author : A. Bialynicki-Birula
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algebraic Quotients Torus Actions And Cohomology The Adjoint Representation And The Adjoint Action written by A. Bialynicki-Birula 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 2013-03-09 with Mathematics categories.
This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.
Lie Groups And Invariant Theory
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Author : Ėrnest Borisovich Vinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Lie Groups And Invariant Theory written by Ėrnest Borisovich Vinberg 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 2005 with Computers categories.
This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.
Conjugacy Classes In Semisimple Algebraic Groups
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Author : James E. Humphreys
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Conjugacy Classes In Semisimple Algebraic Groups written by James E. Humphreys 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 1995 with Education categories.
Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.
Groups Of Exceptional Type Coxeter Groups And Related Geometries
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Author : N.S. Narasimha Sastry
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-02
Groups Of Exceptional Type Coxeter Groups And Related Geometries written by N.S. Narasimha Sastry 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 2014-04-02 with Mathematics categories.
The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.
Algebraic Transformation Groups And Algebraic Varieties
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Author : Vladimir Leonidovich Popov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Algebraic Transformation Groups And Algebraic Varieties written by Vladimir Leonidovich Popov 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 2013-06-29 with Mathematics categories.
The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.
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 Mathematics 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.