Schur Weyl Dualities For Lie Superalgebras And Lie Color Algebras
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Schur Weyl Dualities For Lie Superalgebras And Lie Color Algebras
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Author : Dongho Moon
language : en
Publisher:
Release Date : 1998
Schur Weyl Dualities For Lie Superalgebras And Lie Color Algebras written by Dongho Moon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Dualities And Representations Of Lie Superalgebras
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Author : Shun-Jen Cheng
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Dualities And Representations Of Lie Superalgebras written by Shun-Jen Cheng 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 2012 with Mathematics categories.
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.
Imaginary Schur Weyl Duality
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Author : Alexander Kleshchev
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
Imaginary Schur Weyl Duality written by Alexander Kleshchev 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 2017-01-18 with Duality theory (Mathematics) categories.
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules—one for each real positive root for the corresponding affine root system X , as well as irreducible imaginary modules—one for each -multiplication. The authors study imaginary modules by means of “imaginary Schur-Weyl duality” and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
Recent Progress In Algebra
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Author : Sang Geun Hahn
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Recent Progress In Algebra written by Sang Geun Hahn 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 1999 with Mathematics categories.
This volume presents the proceedings of the international conference on "Recent Progress in Algebra" that was held at the Korea Advanced Institute of Science and Technology (KAIST) and Korea Institute for Advanced Study (KIAS). It brought together experts in the field to discuss progress in algebra, combinatorics, algebraic geometry and number theory. This book contains selected papers contributed by conference participants. The papers cover a wide range of topics and reflect the current state of research in modern algebra.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 1999
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Dissertations, Academic categories.
Advances In Quantum Computation
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Author : Kazem Mahdavi
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-01
Advances In Quantum Computation written by Kazem Mahdavi 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 2009-04-01 with Mathematics categories.
This volume represents the talks given at the Conference on Interactions between Representation Theory, Quantum Field Theory, Category Theory, Mathematical Physics, and Quantum Information Theory, held in September 2007 at the University of Texas at Tyler. The papers in this volume, written by top experts in the field, address physical aspects, mathematical aspects, and foundational issues of quantum computation. This volume will benefit researchers interested in advances in quantum computation and communication, as well as graduate students who wish to enter the field of quantum computation.
Lie Groups
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Author : Daniel Bump
language : en
Publisher:
Release Date : 2013-10-31
Lie Groups written by Daniel Bump and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-31 with categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Dictionary On Lie Algebras And Superalgebras
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Author : Luc Frappat
language : en
Publisher:
Release Date : 2000
Dictionary On Lie Algebras And Superalgebras written by Luc Frappat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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
The Q Schur Algebra
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Author : Stephen Donkin
language : en
Publisher: Cambridge University Press
Release Date : 1998-12-10
The Q Schur Algebra written by Stephen Donkin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-10 with Mathematics categories.
This book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. The aim is to present, from a unified point of view, quantum analogs of certain results known already in the classical case. The approach is largely homological, based on Kempf's vanishing theorem for quantum groups and the quasi-hereditary structure of the q-Schur algebras. Beginning with an introductory chapter dealing with the relationship between the ordinary general linear groups and their quantum analogies, the text goes on to discuss the Schur Functor and the 0-Schur algebra. The next chapter considers Steinberg's tensor product and infinitesimal theory. Later sections of the book discuss tilting modules, the Ringel dual of the q-Schur algebra, Specht modules for Hecke algebras, and the global dimension of the q-Schur algebras. An appendix gives a self-contained account of the theory of quasi-hereditary algebras and their associated tilting modules. This volume will be primarily of interest to researchers in algebra and related topics in pure mathematics.