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Author : James Lepowsky
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (15 download)
Download or read book Structure of the Standard Modules for the Affine Lie Algebra A1 Superscript (1) written by James Lepowsky and published by . This book was released on 1985 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Lepowsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821850482
Total Pages : 96 pages
Book Rating : 4.8/5 (218 download)
Download or read book Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$ written by James Lepowsky and published by American Mathematical Soc.. This book was released on 1985 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The affine Kac-Moody algebra $A_1 DEGREES{(1)}$ has served as a source of ideas in the representation theory of infinite-dimensional affine Lie algebras. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1 DEGREES{(1)}$-modules in the homogeneou
Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (123 download)
Download or read book Structure of the Standard Modules for the Affine Lie Algebra A Subscript 1 Superscript(1). written by Mathematical Sciences Research Institute (Berkeley, Calif.). and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marly Mandia
Publisher : American Mathematical Soc.
ISBN 13 : 0821824236
Total Pages : 161 pages
Book Rating : 4.8/5 (218 download)
Download or read book Structures of the Level One Standard Modules for the Affine Lie Algebras $B_l^{(1)}$, $F_4^{(1)}$, and $G_2^{(1)}$ written by Marly Mandia and published by American Mathematical Soc.. This book was released on 1987 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
, F4(1), and G2(1) PDF Online Free](https://books.google.com/books/content/images/frontcover/_33kwAEACAAJ?fife=w200-h370)
Author : Frank Rimlinger
Publisher :
ISBN 13 : 9780821824207
Total Pages : 54 pages
Book Rating : 4.8/5 (242 download)
Download or read book Structure of the Level One Standard Modules for the Affine Lie Algebras B[subscript L](1), F4(1), and G2(1) written by Frank Rimlinger and published by . This book was released on 1987 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel J. Britten
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860090
Total Pages : 398 pages
Book Rating : 4.8/5 (6 download)
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.
Author : Georgia Benkart
Publisher : American Mathematical Soc.
ISBN 13 : 0821851195
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Author : Christopher Michael Sadowski
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (889 download)
Download or read book On the Structure of Principal Subspaces of Standard Modules for Affine Lie Algebras of Type A written by Christopher Michael Sadowski and published by . This book was released on 2014 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the theory of vertex operator algebras and intertwining operators, we obtain presentations for the principal subspaces of all the standard $widehat{goth{sl}(3)}$-modules. Certain of these presentations had been conjectured and used in work of Calinescu to construct exact sequences leading to the graded dimensions of certain principal subspaces. We prove the conjecture in its full generality for all standard $widehat{goth{sl}(3)}$-modules. We then provide a conjecture for the case of $widehat{goth{sl}(n)}$, $n ge 4$. In addition, we construct completions of certain universal enveloping algebras and provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex operator algebras and intertwining operators, along with conjecturally assumed presentations for certain principal subspaces, to construct exact sequences among principal subspaces of certain standard $widehat{mathfrak{sl}(n)}$-modules, $n ge 3$. As a consequence, we obtain the multigraded dimensions of the principal subspaces $W(k_1Lambda_1 + k_2 Lambda_2)$ and $W(k_{n-2}Lambda_{n-2} + k_{n-1} Lambda_{n-1})$. This generalizes earlier work by Calinescu on principal subspaces of standard $widehat{mathfrak{sl}(3)}$-modules, where similar assumptions were made.
Author : Dražen Adamović
Publisher : Springer Nature
ISBN 13 : 3030329062
Total Pages : 218 pages
Book Rating : 4.0/5 (33 download)
Download or read book Affine, Vertex and W-algebras written by Dražen Adamović and published by Springer Nature. This book was released on 2019-11-28 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.
Author : Yi-Zhi Huang
Publisher : American Mathematical Soc.
ISBN 13 : 0821839861
Total Pages : 500 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lie Algebras, Vertex Operator Algebras and Their Applications written by Yi-Zhi Huang and published by American Mathematical Soc.. This book was released on 2007 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
Author : J. Lepowsky
Publisher : Springer Science & Business Media
ISBN 13 : 146139550X
Total Pages : 484 pages
Book Rating : 4.4/5 (613 download)
Download or read book Vertex Operators in Mathematics and Physics written by J. Lepowsky and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Author : Robert Wisbauer
Publisher : CRC Press
ISBN 13 : 9780582289819
Total Pages : 384 pages
Book Rating : 4.2/5 (898 download)
Download or read book Modules and Algebras written by Robert Wisbauer and published by CRC Press. This book was released on 1996-05-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.
Author : Arne Meurman
Publisher : American Mathematical Soc.
ISBN 13 : 0821809237
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)
Download or read book Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities written by Arne Meurman and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\frak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\frak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\frak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\frak g}$ is of type $A{(1)} 1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.
Author :
Publisher :
ISBN 13 :
Total Pages : 708 pages
Book Rating : 4.3/5 (91 download)
Download or read book Glasnik Matematički written by and published by . This book was released on 1998 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Jimbo
Publisher : Elsevier
ISBN 13 : 1483295257
Total Pages : 695 pages
Book Rating : 4.4/5 (832 download)
Download or read book Integrable Systems in Quantum Field Theory and Statistical Mechanics written by M. Jimbo and published by Elsevier. This book was released on 2014-05-19 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Sys Quantum Field Theory
Author : H Saleur
Publisher : World Scientific
ISBN 13 : 9814549991
Total Pages : 346 pages
Book Rating : 4.8/5 (145 download)
Download or read book Recent Progress In Statistical Mechanics And Quantum Field Theory written by H Saleur and published by World Scientific. This book was released on 1995-08-31 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following topics were covered: the study of renormalization group flows between field theories using the methods of quantum integrability, S-matrix theory and the thermodynamic Bethe Ansatz; impurity problems approached both from the point of view of conformal field theory and quantum integrability. This includes the Kondo effect and quantum wires; solvable models with 1/r² interactions (Haldane-Shastri models). Yangian symmetries in 1/r² models and in conformal field theories; correlation functions in integrable 1+1 field theories; integrability in three dimensions; conformal invariance and the quantum hall effect; supersymmetry in statistical mechanics; and relations to two-dimensional Yang-Mills and QCD.
Author : D. Winter
Publisher : Springer
ISBN 13 : 3540392629
Total Pages : 243 pages
Book Rating : 4.5/5 (43 download)
Download or read book Lie Algebras and Related Topics written by D. Winter and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
