Dualities And Representations Of Lie Superalgebras

Author : Shun-Jen Cheng,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 46,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891186

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Dualities and Representations of Lie Superalgebras by Shun-Jen Cheng,Weiqiang Wang Pdf

This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

Author : Dongho Moon
Publisher : Unknown
Page : 244 pages
File Size : 48,9 Mb
Release : 1998
Category : Electronic
ISBN : WISC:89063826648

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Schur-Weyl Dualities for Lie Superalgebras and Lie Color Algebras by Dongho Moon Pdf

Author : Ian Malcolm Musson
Publisher : American Mathematical Soc.
Page : 512 pages
File Size : 43,6 Mb
Release : 2012-04-04
Category : Mathematics
ISBN : 9780821868676

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Lie Superalgebras and Enveloping Algebras by Ian Malcolm Musson Pdf

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.

Author : M. Scheunert
Publisher : Springer
Page : 280 pages
File Size : 53,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540352860

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The Theory of Lie Superalgebras by M. Scheunert Pdf

Author : Maria Gorelik,Paolo Papi
Publisher : Springer Science & Business
Page : 280 pages
File Size : 53,9 Mb
Release : 2014-04-28
Category : Mathematics
ISBN : 9783319029528

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Advances in Lie Superalgebras by Maria Gorelik,Paolo Papi Pdf

The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.

Author : Naihuan Jing,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 48,9 Mb
Release : 2018-08-21
Category : Algebra
ISBN : 9781470436964

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Representations of Lie Algebras, Quantum Groups and Related Topics by Naihuan Jing,Kailash C. Misra Pdf

This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.

Author : Geoffrey Mason,Ivan Penkov,Joseph A. Wolf
Publisher : Springer
Page : 397 pages
File Size : 49,5 Mb
Release : 2014-10-31
Category : Mathematics
ISBN : 9783319098043

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Developments and Retrospectives in Lie Theory by Geoffrey Mason,Ivan Penkov,Joseph A. Wolf Pdf

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Author : Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 55,9 Mb
Release : 2016-06-28
Category : Group theory and generalizations
ISBN : 9781470418441

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Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics by Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall Pdf

This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Author : Luc Frappat,Antonino Sciarrino,Paul Sorba
Publisher : Unknown
Page : 440 pages
File Size : 51,6 Mb
Release : 2000
Category : Mathematics
ISBN : UOM:39015036038282

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Dictionary on Lie Algebras and Superalgebras by Luc Frappat,Antonino Sciarrino,Paul Sorba Pdf

This book is a detailed reference on Lie algebras and Lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike. Key Features: * Compiles and presents material currently scattered throughout numerous textbooks and specialist journal articles * Dictionary format provides an easy to use reference on the essential topics concerning Lie algebras and Lie superalgebras * Covers the structure of Lie algebras and Lie superalgebras and their finite dimensional representation theory * Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras

Author : Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Publisher : Springer
Page : 461 pages
File Size : 42,9 Mb
Release : 2017-12-07
Category : Mathematics
ISBN : 9783319589718

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Perspectives in Lie Theory by Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole Pdf

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 40,6 Mb
Release : 2004
Category : Mathematics
ISBN : 0817633731

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Lie Theory by Jean-Philippe Anker,Bent Orsted Pdf

* 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.

Author : Ivan Penkov,Crystal Hoyt
Publisher : Springer Nature
Page : 245 pages
File Size : 55,9 Mb
Release : 2022-01-05
Category : Mathematics
ISBN : 9783030896607

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Classical Lie Algebras at Infinity by Ivan Penkov,Crystal Hoyt Pdf

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.

Author : Swanhild Bernstein
Publisher : Springer Nature
Page : 503 pages
File Size : 42,7 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9783030238544

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Topics in Clifford Analysis by Swanhild Bernstein Pdf

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.

Author : Jens Gerlach Christensen,Susanna Dann,Matthew Dawson
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 41,5 Mb
Release : 2018-08-27
Category : Festschriften
ISBN : 9781470440701

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Representation Theory and Harmonic Analysis on Symmetric Spaces by Jens Gerlach Christensen,Susanna Dann,Matthew Dawson Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.

Author : Kailash C. Misra,Daniel Ken Nakano,Brian Parshall
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 52,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869178

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Recent Developments in Lie Algebras, Groups and Representation Theory by Kailash C. Misra,Daniel Ken Nakano,Brian Parshall Pdf

This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.