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Representations And Nilpotent Orbits Of Lie Algebraic Systems
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Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik
Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
Book Synopsis Nilpotent Orbits In Semisimple Lie Algebra by : William.M. McGovern
Download or read book Nilpotent Orbits In Semisimple Lie Algebra written by William.M. McGovern and published by Routledge. This book was released on 2017-10-19 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Representation Theory and Extended Affine Lie Algebras by : Erhard Neher
Download or read book Geometric Representation Theory and Extended Affine Lie Algebras written by Erhard Neher and published by American Mathematical Soc.. This book was released on 2011 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.
Book Synopsis Nilpotent Orbits, Primitive Ideals, and Characteristic Classes by : Walter Borho
Download or read book Nilpotent Orbits, Primitive Ideals, and Characteristic Classes written by Walter Borho and published by . This book was released on 1989-12-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras by : Martin W. Liebeck
Download or read book Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2012-01-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
Book Synopsis Representations of Nilpotent Lie Algebras and Superalgebras by : Shantala Mukherjee
Download or read book Representations of Nilpotent Lie Algebras and Superalgebras written by Shantala Mukherjee and published by . This book was released on 2004 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Group Representations by : R.L. Lipsman
Download or read book Group Representations written by R.L. Lipsman and published by Springer. This book was released on 2006-08-01 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integrable Systems on Lie Algebras and Symmetric Spaces by : A. T. Fomenko
Download or read book Integrable Systems on Lie Algebras and Symmetric Spaces written by A. T. Fomenko and published by CRC Press. This book was released on 1988 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Nilpotent Orbits, Associated Cycles and Whittaker Models for Highest Weight Representations by : Kyo Nishiyama
Download or read book Nilpotent Orbits, Associated Cycles and Whittaker Models for Highest Weight Representations written by Kyo Nishiyama and published by . This book was released on 2001 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soit G un groupe de Lie réductif de type hermitien. Nous étudions les représentations irréductibles (unitaires) de G de plus haut poids, qui ne sont pas nécessairement dans la série discrète holomorphe. Les résultats obtenus dans les trois articles de ce volume comprennent la détermination des cycles associés, des degrés de Bernstein et des modèles de Whittaker généralisés de ces représentations. Nous donnons une description commode des K-types par les règles de branchement des représentations des groupes classiques. Une formule intégrale pour les degrés des petites orbites nilpotentes est établie pour les algèbres de Lie hermitiennes quelconques. Les modèles de Whittaker généralisés pour chaque module unitaire de plus haut poids sont spécifiés au moyen du symbole principal d'un opérateur différentiel de type gradient, et également en relation avec la multiplicité dans le cycle associé. Le texte comporte aussi des exposés introductifs concernant les principales notions considérées : cycles associés, correspondance de Howe dans le cas où la paire duale contient un membre compact et réalisation des représentations de plus haut poids dans les noyaux d'opérateurs différentiels de type gradient.
Book Synopsis Lie Algebras and Related Topics by : Daniel J. Britten
Download or read book Lie Algebras and Related Topics written by Daniel J. Britten and published by American Mathematical Soc.. This book was released on 1986 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
Book Synopsis Representations of Algebraic Groups, Quantum Groups and Lie Algebras by : Georgia Benkart
Download or read book Representations of Algebraic Groups, Quantum Groups and Lie Algebras written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 2006 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains several well-written accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental in representation theory, and the proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.
Book Synopsis Nilpotent Orbits in Bad Characteristic and the Springer Correspondence by : Ting Xue (Ph. D.)
Download or read book Nilpotent Orbits in Bad Characteristic and the Springer Correspondence written by Ting Xue (Ph. D.) and published by . This book was released on 2010 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p, g the Lie algebra of G and g* the dual vector space of g. This thesis is concerned with nilpotent orbits in g and g* and the Springer correspondence for g and g* when p is a bad prime. Denote W the set of isomorphism classes of irreducible representations of the Weyl group W of G. Fix a prime number 1 7 p. We denote ... the set of all pairs (c, F), where c is a nilpotent G-orbit in g (resp. g*) and F is an irreducible G-equivariant Q1-local system on c (up to isomorphism). In chapter 1, we study the Springer correspondence for g when G is of type B, C or D (p = 2). The correspondence is a bijective map from W to 2t.. In particular, we classify nilpotent G-orbits in g (type B, D) over finite fields of characteristic 2. In chapter 2, we study the Springer correspondence for g* when G is of type B, C or D (p = 2). The correspondence is a bijective map from ... In particular, we classify nilpotent G-orbits in g* over algebraically closed and finite fields of characteristic 2. In chapter 3, we give a combinatorial description of the Springer correspondence constructed in chapter 1 and chapter 2 for 8 and g*. In chapter 4, we study the nilpotent orbits in 8* and the Weyl group representations that correspond to the pairs ... under Springer correspondence when G is of an exceptional type. Chapters 1, 2 and 3 are based on the papers [X1, X2, X3]. Chapter 4 is based on some unpublished work.
Book Synopsis On Lie Algebras and Some Special Functions of Mathematical Physics by : Willard Miller
Download or read book On Lie Algebras and Some Special Functions of Mathematical Physics written by Willard Miller and published by American Mathematical Soc.. This book was released on 1964 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical Lie Algebras at Infinity by : Ivan Penkov
Download or read book Classical Lie Algebras at Infinity written by Ivan Penkov and published by Springer Nature. This book was released on 2022-01-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Book Synopsis The Lie Algebras su(N) by : Walter Pfeifer
Download or read book The Lie Algebras su(N) written by Walter Pfeifer and published by Springer Science & Business Media. This book was released on 2003-07-23 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie algebras are efficient tools for analyzing the properties of physical systems. Concrete applications comprise the formulation of symmetries of Hamiltonian systems, the description of atomic, molecular and nuclear spectra, the physics of elementary particles and many others. This work gives an introduction to the properties and the structure of the Lie algebras su(n). The book features an elementary (matrix) access to su(N)-algebras, and gives a first insight into Lie algebras. Student readers should be enabled to begin studies on physical su(N)-applications, instructors will profit from the detailed calculations and examples.
Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer. This book was released on 2016-12-10 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
